Complex Non Kähler Geometry

Author : Sławomir Dinew,Sebastien Picard,Andrei Teleman,Alberto Verjovsky
Publisher : Springer Nature
Page : 242 pages
File Size : 45,6 Mb
Release : 2019-11-05
Category : Mathematics
ISBN : 9783030258832

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Complex Non-Kähler Geometry by Sławomir Dinew,Sebastien Picard,Andrei Teleman,Alberto Verjovsky Pdf

Collecting together the lecture notes of the CIME Summer School held in Cetraro in July 2018, the aim of the book is to introduce a vast range of techniques which are useful in the investigation of complex manifolds. The school consisted of four courses, focusing on both the construction of non-Kähler manifolds and the understanding of a possible classification of complex non-Kähler manifolds. In particular, the courses by Alberto Verjovsky and Andrei Teleman introduced tools in the theory of foliations and analytic techniques for the classification of compact complex surfaces and compact Kähler manifolds, respectively. The courses by Sebastien Picard and Sławomir Dinew focused on analytic techniques in Hermitian geometry, more precisely, on special Hermitian metrics and geometric flows, and on pluripotential theory in complex non-Kähler geometry.

Author : Daniele Angella
Publisher : Springer
Page : 289 pages
File Size : 40,5 Mb
Release : 2013-11-22
Category : Mathematics
ISBN : 9783319024417

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Cohomological Aspects in Complex Non-Kähler Geometry by Daniele Angella Pdf

In these notes, we provide a summary of recent results on the cohomological properties of compact complex manifolds not endowed with a Kähler structure. On the one hand, the large number of developed analytic techniques makes it possible to prove strong cohomological properties for compact Kähler manifolds. On the other, in order to further investigate any of these properties, it is natural to look for manifolds that do not have any Kähler structure. We focus in particular on studying Bott-Chern and Aeppli cohomologies of compact complex manifolds. Several results concerning the computations of Dolbeault and Bott-Chern cohomologies on nilmanifolds are summarized, allowing readers to study explicit examples. Manifolds endowed with almost-complex structures, or with other special structures (such as, for example, symplectic, generalized-complex, etc.), are also considered.

Author : Daniele Angella
Publisher : Unknown
Page : 292 pages
File Size : 40,5 Mb
Release : 2013-12-31
Category : Electronic
ISBN : 3319024426

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Cohomological Aspects in Complex Non-Kahler Geometry by Daniele Angella Pdf

Author : Daniele Angella,Costantino Medori,Adriano Tomassini
Publisher : Springer
Page : 262 pages
File Size : 50,5 Mb
Release : 2017-10-12
Category : Mathematics
ISBN : 9783319629148

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Complex and Symplectic Geometry by Daniele Angella,Costantino Medori,Adriano Tomassini Pdf

This book arises from the INdAM Meeting "Complex and Symplectic Geometry", which was held in Cortona in June 2016. Several leading specialists, including young researchers, in the field of complex and symplectic geometry, present the state of the art of their research on topics such as the cohomology of complex manifolds; analytic techniques in Kähler and non-Kähler geometry; almost-complex and symplectic structures; special structures on complex manifolds; and deformations of complex objects. The work is intended for researchers in these areas.

Author : Liviu Ornea,Misha Verbitsky
Publisher : Springer Nature
Page : 729 pages
File Size : 45,5 Mb
Release : 2024
Category : Kählerian manifolds
ISBN : 9783031581205

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Principles of Locally Conformally Kähler Geometry by Liviu Ornea,Misha Verbitsky Pdf

This monograph introduces readers to locally conformally Kähler (LCK) geometry and provides an extensive overview of the most current results. A rapidly developing area in complex geometry dealing with non-Kähler manifolds, LCK geometry has strong links to many other areas of mathematics, including algebraic geometry, topology, and complex analysis. The authors emphasize these connections to create a unified and rigorous treatment of the subject suitable for both students and researchers. Part I builds the necessary foundations for those approaching LCK geometry for the first time with full, mostly self-contained proofs and also covers material often omitted from textbooks, such as contact and Sasakian geometry, orbifolds, Ehresmann connections, and foliation theory. More advanced topics are then treated in Part II, including non-Kähler elliptic surfaces, cohomology of holomorphic vector bundles on Hopf manifolds, Kuranishi and Teichmüller spaces for LCK manifolds with potential, and harmonic forms on Sasakian and Vaisman manifolds. Each chapter in Parts I and II begins with motivation and historic context for the topics explored and includes numerous exercises for further exploration of important topics. Part III surveys the current research on LCK geometry, describing advances on topics such as automorphism groups on LCK manifolds, twisted Hamiltonian actions and LCK reduction, Einstein-Weyl manifolds and the Futaki invariant, and LCK geometry on nilmanifolds and on solvmanifolds. New proofs of many results are given using the methods developed earlier in the text. The text then concludes with a chapter that gathers over 100 open problems, with context and remarks provided where possible, to inspire future research. .

Author : Daniel Huybrechts
Publisher : Springer Science & Business Media
Page : 336 pages
File Size : 46,6 Mb
Release : 2005
Category : Computers
ISBN : 3540212906

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Complex Geometry by Daniel Huybrechts Pdf

Easily accessible Includes recent developments Assumes very little knowledge of differentiable manifolds and functional analysis Particular emphasis on topics related to mirror symmetry (SUSY, Kaehler-Einstein metrics, Tian-Todorov lemma)

Author : Gang Tian
Publisher : Birkhäuser
Page : 107 pages
File Size : 41,6 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783034883894

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Canonical Metrics in Kähler Geometry by Gang Tian Pdf

There has been fundamental progress in complex differential geometry in the last two decades. For one, The uniformization theory of canonical Kähler metrics has been established in higher dimensions, and many applications have been found, including the use of Calabi-Yau spaces in superstring theory. This monograph gives an introduction to the theory of canonical Kähler metrics on complex manifolds. It also presents some advanced topics not easily found elsewhere.

Author : Andrei Moroianu
Publisher : Cambridge University Press
Page : 4 pages
File Size : 47,8 Mb
Release : 2007-03-29
Category : Mathematics
ISBN : 9781139463003

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Lectures on Kähler Geometry by Andrei Moroianu Pdf

Kähler geometry is a beautiful and intriguing area of mathematics, of substantial research interest to both mathematicians and physicists. This self-contained graduate text provides a concise and accessible introduction to the topic. The book begins with a review of basic differential geometry, before moving on to a description of complex manifolds and holomorphic vector bundles. Kähler manifolds are discussed from the point of view of Riemannian geometry, and Hodge and Dolbeault theories are outlined, together with a simple proof of the famous Kähler identities. The final part of the text studies several aspects of compact Kähler manifolds: the Calabi conjecture, Weitzenböck techniques, Calabi–Yau manifolds, and divisors. All sections of the book end with a series of exercises and students and researchers working in the fields of algebraic and differential geometry and theoretical physics will find that the book provides them with a sound understanding of this theory.

Author : Gábor Székelyhidi
Publisher : American Mathematical Soc.
Page : 210 pages
File Size : 43,6 Mb
Release : 2014-06-19
Category : Mathematics
ISBN : 9781470410476

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An Introduction to Extremal Kahler Metrics by Gábor Székelyhidi Pdf

A basic problem in differential geometry is to find canonical metrics on manifolds. The best known example of this is the classical uniformization theorem for Riemann surfaces. Extremal metrics were introduced by Calabi as an attempt at finding a higher-dimensional generalization of this result, in the setting of Kähler geometry. This book gives an introduction to the study of extremal Kähler metrics and in particular to the conjectural picture relating the existence of extremal metrics on projective manifolds to the stability of the underlying manifold in the sense of algebraic geometry. The book addresses some of the basic ideas on both the analytic and the algebraic sides of this picture. An overview is given of much of the necessary background material, such as basic Kähler geometry, moment maps, and geometric invariant theory. Beyond the basic definitions and properties of extremal metrics, several highlights of the theory are discussed at a level accessible to graduate students: Yau's theorem on the existence of Kähler-Einstein metrics, the Bergman kernel expansion due to Tian, Donaldson's lower bound for the Calabi energy, and Arezzo-Pacard's existence theorem for constant scalar curvature Kähler metrics on blow-ups.

Author : Werner Ballmann
Publisher : European Mathematical Society
Page : 190 pages
File Size : 51,7 Mb
Release : 2006
Category : Mathematics
ISBN : 3037190256

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Lectures on Kähler Manifolds by Werner Ballmann Pdf

These notes are based on lectures the author gave at the University of Bonn and the Erwin Schrodinger Institute in Vienna. The aim is to give a thorough introduction to the theory of Kahler manifolds with special emphasis on the differential geometric side of Kahler geometry. The exposition starts with a short discussion of complex manifolds and holomorphic vector bundles and a detailed account of the basic differential geometric properties of Kahler manifolds. The more advanced topics are the cohomology of Kahler manifolds, Calabi conjecture, Gromov's Kahler hyperbolic spaces, and the Kodaira embedding theorem. Some familiarity with global analysis and partial differential equations is assumed, in particular in the part on the Calabi conjecture. There are appendices on Chern-Weil theory, symmetric spaces, and $L^2$-cohomology.

Author : Mario Garcia-Fernandez,Jeffrey Streets
Publisher : American Mathematical Soc.
Page : 248 pages
File Size : 53,7 Mb
Release : 2021-04-06
Category : Education
ISBN : 9781470462581

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Generalized Ricci Flow by Mario Garcia-Fernandez,Jeffrey Streets Pdf

The generalized Ricci flow is a geometric evolution equation which has recently emerged from investigations into mathematical physics, Hitchin's generalized geometry program, and complex geometry. This book gives an introduction to this new area, discusses recent developments, and formulates open questions and conjectures for future study. The text begins with an introduction to fundamental aspects of generalized Riemannian, complex, and Kähler geometry. This leads to an extension of the classical Einstein-Hilbert action, which yields natural extensions of Einstein and Calabi-Yau structures as ‘canonical metrics’ in generalized Riemannian and complex geometry. The book then introduces generalized Ricci flow as a tool for constructing such metrics and proves extensions of the fundamental Hamilton/Perelman regularity theory of Ricci flow. These results are refined in the setting of generalized complex geometry, where the generalized Ricci flow is shown to preserve various integrability conditions, taking the form of pluriclosed flow and generalized Kähler-Ricci flow, leading to global convergence results and applications to complex geometry. Finally, the book gives a purely mathematical introduction to the physical idea of T-duality and discusses its relationship to generalized Ricci flow. The book is suitable for graduate students and researchers with a background in Riemannian and complex geometry who are interested in the theory of geometric evolution equations.

Author : Daniel Huybrechts
Publisher : Springer Science & Business Media
Page : 321 pages
File Size : 43,8 Mb
Release : 2005-09-02
Category : Mathematics
ISBN : 9783540266877

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Complex Geometry by Daniel Huybrechts Pdf

Easily accessible Includes recent developments Assumes very little knowledge of differentiable manifolds and functional analysis Particular emphasis on topics related to mirror symmetry (SUSY, Kaehler-Einstein metrics, Tian-Todorov lemma)

Author : Sorin Dragomir,Liuiu Ornea
Publisher : Springer Science & Business Media
Page : 332 pages
File Size : 43,5 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461220268

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Locally Conformal Kähler Geometry by Sorin Dragomir,Liuiu Ornea Pdf

. E C, 0 1'1 1, and n E Z, n ~ 2. Let~.. be the O-dimensional Lie n group generated by the transformation z ~ >.z, z E C - {a}. Then (cf.

Author : Nigel J. Hitchin
Publisher : Oxford University Press
Page : 453 pages
File Size : 52,7 Mb
Release : 2010-07
Category : Mathematics
ISBN : 9780199534920

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The Many Facets of Geometry by Nigel J. Hitchin Pdf

This title celebrates the academic career of Professor Nigel Hitchin - one of the most influential figures in the field of differential and algebraic geometry.

Author : Jingyi Chen,Peng Lu,Zhiqin Lu,Zhou Zhang
Publisher : Springer Nature
Page : 616 pages
File Size : 54,6 Mb
Release : 2020-04-10
Category : Mathematics
ISBN : 9783030349530

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Geometric Analysis by Jingyi Chen,Peng Lu,Zhiqin Lu,Zhou Zhang Pdf

This edited volume has a two-fold purpose. First, comprehensive survey articles provide a way for beginners to ease into the corresponding sub-fields. These are then supplemented by original works that give the more advanced readers a glimpse of the current research in geometric analysis and related PDEs. The book is of significant interest for researchers, including advanced Ph.D. students, working in geometric analysis. Readers who have a secondary interest in geometric analysis will benefit from the survey articles. The results included in this book will stimulate further advances in the subjects: geometric analysis, including complex differential geometry, symplectic geometry, PDEs with a geometric origin, and geometry related to topology. Contributions by Claudio Arezzo, Alberto Della Vedova, Werner Ballmann, Henrik Matthiesen, Panagiotis Polymerakis, Sun-Yung A. Chang, Zheng-Chao Han, Paul Yang, Tobias Holck Colding, William P. Minicozzi II, Panagiotis Dimakis, Richard Melrose, Akito Futaki, Hajime Ono, Jiyuan Han, Jeff A. Viaclovsky, Bruce Kleiner, John Lott, Sławomir Kołodziej, Ngoc Cuong Nguyen, Chi Li, Yuchen Liu, Chenyang Xu, YanYan Li, Luc Nguyen, Bo Wang, Shiguang Ma, Jie Qing, Xiaonan Ma, Sean Timothy Paul, Kyriakos Sergiou, Tristan Rivière, Yanir A. Rubinstein, Natasa Sesum, Jian Song, Jeffrey Streets, Neil S. Trudinger, Yu Yuan, Weiping Zhang, Xiaohua Zhu and Aleksey Zinger.