Some Questions Of Differential Geometry In The Large

Author : E. V. Shikin
Publisher : American Mathematical Soc.
Page : 208 pages
File Size : 53,6 Mb
Release : 1996-07-16
Category : Electronic
ISBN : 0821895974

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Some questions of differential geometry in the large by E. V. Shikin Pdf

This collection contains articles that present recent results by geometers in Russia and the Ukraine. Papers in the collection deal with various questions related to the structure, symmetries, and embeddings of submanifolds in Euclidean and pseudo-Euclidian spaces. This collection offers a review of the challenges facing specialists in geometry in the large and features current research in the field.

Author : Heinz Hopf
Publisher : Springer
Page : 192 pages
File Size : 45,6 Mb
Release : 2003-07-01
Category : Mathematics
ISBN : 9783540394822

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Differential Geometry in the Large by Heinz Hopf Pdf

These notes consist of two parts: Selected in York 1) Geometry, New 1946, Topics University Notes Peter Lax. by Differential in the 2) Lectures on Stanford Geometry Large, 1956, Notes J.W. University by Gray. are here with no essential They reproduced change. Heinz was a mathematician who mathema- Hopf recognized important tical ideas and new mathematical cases. In the phenomena through special the central idea the of a or difficulty problem simplest background is becomes clear. in this fashion a crystal Doing geometry usually lead serious allows this to to - joy. Hopf's great insight approach for most of the in these notes have become the st- thematics, topics I will to mention a of further try ting-points important developments. few. It is clear from these notes that laid the on Hopf emphasis po- differential Most of the results in smooth differ- hedral geometry. whose is both t1al have understanding geometry polyhedral counterparts, works I wish to mention and recent important challenging. Among those of Robert on which is much in the Connelly rigidity, very spirit R. and in - of these notes (cf. Connelly, Conjectures questions open International of Mathematicians, H- of gidity, Proceedings Congress sinki vol. 1, 407-414) 1978, .

Author : George A. Duckett
Publisher : Createspace Independent Publishing Platform
Page : 266 pages
File Size : 47,8 Mb
Release : 2015-12-24
Category : Electronic
ISBN : 152290610X

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Differential Geometry by George A. Duckett Pdf

If you have a question about Differential Geometry this is the book with the answers. Differential Geometry: Questions and Answers takes some of the best questions and answers asked on the math.stackexchange.com website. You can use this book to look up commonly asked questions, browse questions on a particular topic, compare answers to common topics, check out the original source and much more. This book has been designed to be very easy to use, with many internal references set up that makes browsing in many different ways possible. Topics covered include: differential topology, manifolds, riemannian gemoetry, differential forms and many more."

Author : Heinz Hopf
Publisher : Unknown
Page : 162 pages
File Size : 40,7 Mb
Release : 1955
Category : Geometry, Differential
ISBN : CORNELL:31924001556558

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Selected Topics in Differential Geometry in the Large by Heinz Hopf Pdf

Author : A.N. Pressley
Publisher : Springer Science & Business Media
Page : 336 pages
File Size : 49,8 Mb
Release : 2013-11-11
Category : Mathematics
ISBN : 9781447136965

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Elementary Differential Geometry by A.N. Pressley Pdf

Pressley assumes the reader knows the main results of multivariate calculus and concentrates on the theory of the study of surfaces. Used for courses on surface geometry, it includes intersting and in-depth examples and goes into the subject in great detail and vigour. The book will cover three-dimensional Euclidean space only, and takes the whole book to cover the material and treat it as a subject in its own right.

Author : Jeffrey M. Lee
Publisher : American Mathematical Society
Page : 671 pages
File Size : 41,6 Mb
Release : 2022-03-08
Category : Mathematics
ISBN : 9781470469825

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Manifolds and Differential Geometry by Jeffrey M. Lee Pdf

Differential geometry began as the study of curves and surfaces using the methods of calculus. In time, the notions of curve and surface were generalized along with associated notions such as length, volume, and curvature. At the same time the topic has become closely allied with developments in topology. The basic object is a smooth manifold, to which some extra structure has been attached, such as a Riemannian metric, a symplectic form, a distinguished group of symmetries, or a connection on the tangent bundle. This book is a graduate-level introduction to the tools and structures of modern differential geometry. Included are the topics usually found in a course on differentiable manifolds, such as vector bundles, tensors, differential forms, de Rham cohomology, the Frobenius theorem and basic Lie group theory. The book also contains material on the general theory of connections on vector bundles and an in-depth chapter on semi-Riemannian geometry that covers basic material about Riemannian manifolds and Lorentz manifolds. An unusual feature of the book is the inclusion of an early chapter on the differential geometry of hypersurfaces in Euclidean space. There is also a section that derives the exterior calculus version of Maxwell's equations. The first chapters of the book are suitable for a one-semester course on manifolds. There is more than enough material for a year-long course on manifolds and geometry.

Author : Barrett O'Neill
Publisher : Academic Press
Page : 422 pages
File Size : 45,9 Mb
Release : 2014-05-12
Category : Mathematics
ISBN : 9781483268118

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Elementary Differential Geometry by Barrett O'Neill Pdf

Elementary Differential Geometry focuses on the elementary account of the geometry of curves and surfaces. The book first offers information on calculus on Euclidean space and frame fields. Topics include structural equations, connection forms, frame fields, covariant derivatives, Frenet formulas, curves, mappings, tangent vectors, and differential forms. The publication then examines Euclidean geometry and calculus on a surface. Discussions focus on topological properties of surfaces, differential forms on a surface, integration of forms, differentiable functions and tangent vectors, congruence of curves, derivative map of an isometry, and Euclidean geometry. The manuscript takes a look at shape operators, geometry of surfaces in E, and Riemannian geometry. Concerns include geometric surfaces, covariant derivative, curvature and conjugate points, Gauss-Bonnet theorem, fundamental equations, global theorems, isometries and local isometries, orthogonal coordinates, and integration and orientation. The text is a valuable reference for students interested in elementary differential geometry.

Author : M. Rahula
Publisher : World Scientific
Page : 200 pages
File Size : 51,8 Mb
Release : 1993
Category : Mathematics
ISBN : 9810208197

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New Problems in Differential Geometry by M. Rahula Pdf

The main theme of this book is the geometrical interpretation of phenomena taking place in Jet spaces in connection with differential equations. This concise volume caters to all mathematicians who wish to deepen their acquaintance with the mathematics of differential geometry.

Author : Owen Dearricott,Wilderich Tuschmann,Yuri Nikolayevsky,Diarmuid Crowley,Thomas Leistner
Publisher : Cambridge University Press
Page : 401 pages
File Size : 53,7 Mb
Release : 2020-10-22
Category : Mathematics
ISBN : 9781108812818

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Differential Geometry in the Large by Owen Dearricott,Wilderich Tuschmann,Yuri Nikolayevsky,Diarmuid Crowley,Thomas Leistner Pdf

From Ricci flow to GIT, physics to curvature bounds, Sasaki geometry to almost formality. This is differential geometry at large.

Author : Marián Fecko
Publisher : Cambridge University Press
Page : 11 pages
File Size : 55,9 Mb
Release : 2006-10-12
Category : Science
ISBN : 9781139458030

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Differential Geometry and Lie Groups for Physicists by Marián Fecko Pdf

Covering subjects including manifolds, tensor fields, spinors, and differential forms, this textbook introduces geometrical topics useful in modern theoretical physics and mathematics. It develops understanding through over 1000 short exercises, and is suitable for advanced undergraduate or graduate courses in physics, mathematics and engineering.

Author : Chris J. Isham
Publisher : Allied Publishers
Page : 308 pages
File Size : 48,9 Mb
Release : 2002
Category : Geometry, Differential
ISBN : 8177643169

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Modern Differential Geometry for Physicists by Chris J. Isham Pdf

Author : J. J. Stoker
Publisher : John Wiley & Sons
Page : 432 pages
File Size : 46,9 Mb
Release : 2011-09-09
Category : Mathematics
ISBN : 9781118165478

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Differential Geometry by J. J. Stoker Pdf

This classic work is now available in an unabridged paperback edition. Stoker makes this fertile branch of mathematics accessible to the nonspecialist by the use of three different notations: vector algebra and calculus, tensor calculus, and the notation devised by Cartan, which employs invariant differential forms as elements in an algebra due to Grassman, combined with an operation called exterior differentiation. Assumed are a passing acquaintance with linear algebra and the basic elements of analysis.

Author : QUDDUS KHAN
Publisher : PHI Learning Pvt. Ltd.
Page : 325 pages
File Size : 44,6 Mb
Release : 2012-09-03
Category : Mathematics
ISBN : 9788120346505

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DIFFERENTIAL GEOMETRY OF MANIFOLDS by QUDDUS KHAN Pdf

Curves and surfaces are objects that everyone can see, and many of the questions that can be asked about them are natural and easily understood. Differential geometry is concerned with the precise mathematical formulation of some of these questions, while trying to answer them using calculus techniques. The geometry of differentiable manifolds with structures is one of the most important branches of modern differential geometry. This well-written book discusses the theory of differential and Riemannian manifolds to help students understand the basic structures and consequent developments. While introducing concepts such as bundles, exterior algebra and calculus, Lie group and its algebra and calculus, Riemannian geometry, submanifolds and hypersurfaces, almost complex manifolds, etc., enough care has been taken to provide necessary details which enable the reader to grasp them easily. The material of this book has been successfully tried in classroom teaching. The book is designed for the postgraduate students of Mathematics. It will also be useful to the researchers working in the field of differential geometry and its applications to general theory of relativity and cosmology, and other applied areas. KEY FEATURES  Provides basic concepts in an easy-to-understand style.  Presents the subject in a natural way.  Follows a coordinate-free approach.  Includes a large number of solved examples and illuminating illustrations.  Gives notes and remarks at appropriate places.

Author : Loring W. Tu
Publisher : Springer Science & Business Media
Page : 426 pages
File Size : 55,8 Mb
Release : 2010-10-05
Category : Mathematics
ISBN : 9781441974006

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An Introduction to Manifolds by Loring W. Tu Pdf

Manifolds, the higher-dimensional analogs of smooth curves and surfaces, are fundamental objects in modern mathematics. Combining aspects of algebra, topology, and analysis, manifolds have also been applied to classical mechanics, general relativity, and quantum field theory. In this streamlined introduction to the subject, the theory of manifolds is presented with the aim of helping the reader achieve a rapid mastery of the essential topics. By the end of the book the reader should be able to compute, at least for simple spaces, one of the most basic topological invariants of a manifold, its de Rham cohomology. Along the way, the reader acquires the knowledge and skills necessary for further study of geometry and topology. The requisite point-set topology is included in an appendix of twenty pages; other appendices review facts from real analysis and linear algebra. Hints and solutions are provided to many of the exercises and problems. This work may be used as the text for a one-semester graduate or advanced undergraduate course, as well as by students engaged in self-study. Requiring only minimal undergraduate prerequisites, 'Introduction to Manifolds' is also an excellent foundation for Springer's GTM 82, 'Differential Forms in Algebraic Topology'.

Author : Gerard Walschap
Publisher : Walter de Gruyter GmbH & Co KG
Page : 365 pages
File Size : 49,7 Mb
Release : 2015-07-01
Category : Mathematics
ISBN : 9783110369540

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Multivariable Calculus and Differential Geometry by Gerard Walschap Pdf

This book offers an introduction to differential geometry for the non-specialist. It includes most of the required material from multivariable calculus, linear algebra, and basic analysis. An intuitive approach and a minimum of prerequisites make it a valuable companion for students of mathematics and physics. The main focus is on manifolds in Euclidean space and the metric properties they inherit from it. Among the topics discussed are curvature and how it affects the shape of space, and the generalization of the fundamental theorem of calculus known as Stokes' theorem.