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Metric Structures in Differential Geometry by Gerard Walschap Pdf
This book offers an introduction to the theory of differentiable manifolds and fiber bundles. It examines bundles from the point of view of metric differential geometry: Euclidean bundles, Riemannian connections, curvature, and Chern-Weil theory are discussed, including the Pontrjagin, Euler, and Chern characteristic classes of a vector bundle. These concepts are illustrated in detail for bundles over spheres.
Metric Structures for Riemannian and Non-Riemannian Spaces by Mikhail Gromov Pdf
This book is an English translation of the famous "Green Book" by Lafontaine and Pansu (1979). It has been enriched and expanded with new material to reflect recent progress. Additionally, four appendices, by Gromov on Levy's inequality, by Pansu on "quasiconvex" domains, by Katz on systoles of Riemannian manifolds, and by Semmes overviewing analysis on metric spaces with measures, as well as an extensive bibliography and index round out this unique and beautiful book.
Differential Geometric Structures by Walter A. Poor Pdf
This introductory text defines geometric structure by specifying parallel transport in an appropriate fiber bundle and focusing on simplest cases of linear parallel transport in a vector bundle. 1981 edition.
Differential Geometry and Analysis on CR Manifolds by Sorin Dragomir,Giuseppe Tomassini Pdf
Presents many major differential geometric acheivements in the theory of CR manifolds for the first time in book form Explains how certain results from analysis are employed in CR geometry Many examples and explicitly worked-out proofs of main geometric results in the first section of the book making it suitable as a graduate main course or seminar textbook Provides unproved statements and comments inspiring further study
Transformation Groups in Differential Geometry by Shoshichi Kobayashi Pdf
Given a mathematical structure, one of the basic associated mathematical objects is its automorphism group. The object of this book is to give a biased account of automorphism groups of differential geometric struc tures. All geometric structures are not created equal; some are creations of ~ods while others are products of lesser human minds. Amongst the former, Riemannian and complex structures stand out for their beauty and wealth. A major portion of this book is therefore devoted to these two structures. Chapter I describes a general theory of automorphisms of geometric structures with emphasis on the question of when the automorphism group can be given a Lie group structure. Basic theorems in this regard are presented in §§ 3, 4 and 5. The concept of G-structure or that of pseudo-group structure enables us to treat most of the interesting geo metric structures in a unified manner. In § 8, we sketch the relationship between the two concepts. Chapter I is so arranged that the reader who is primarily interested in Riemannian, complex, conformal and projective structures can skip §§ 5, 6, 7 and 8. This chapter is partly based on lec tures I gave in Tokyo and Berkeley in 1965.
Special Metrics and Group Actions in Geometry by Simon G. Chiossi,Anna Fino,Emilio Musso,Fabio Podestà,Luigi Vezzoni Pdf
The volume is a follow-up to the INdAM meeting “Special metrics and quaternionic geometry” held in Rome in November 2015. It offers a panoramic view of a selection of cutting-edge topics in differential geometry, including 4-manifolds, quaternionic and octonionic geometry, twistor spaces, harmonic maps, spinors, complex and conformal geometry, homogeneous spaces and nilmanifolds, special geometries in dimensions 5–8, gauge theory, symplectic and toric manifolds, exceptional holonomy and integrable systems. The workshop was held in honor of Simon Salamon, a leading international scholar at the forefront of academic research who has made significant contributions to all these subjects. The articles published here represent a compelling testimony to Salamon’s profound and longstanding impact on the mathematical community. Target readership includes graduate students and researchers working in Riemannian and complex geometry, Lie theory and mathematical physics.
Fundamentals of Differential Geometry by Serge Lang Pdf
This book provides an introduction to the basic concepts in differential topology, differential geometry, and differential equations, and some of the main basic theorems in all three areas. This new edition includes new chapters, sections, examples, and exercises. From the reviews: "There are many books on the fundamentals of differential geometry, but this one is quite exceptional; this is not surprising for those who know Serge Lang's books." --EMS NEWSLETTER
The Geometry of Hessian Structures by Hirohiko Shima Pdf
The geometry of Hessian structures is a fascinating emerging field of research. It is in particular a very close relative of Knhlerian geometry, and connected with many important pure mathematical branches such as affine differential geometry, homogeneous spaces and cohomology. The theory also finds deep relation to information geometry in applied mathematics. This systematic introduction to the subject first develops the fundamentals of Hessian structures on the basis of a certain pair of a flat connection and a Riemannian metric, and then describes these related fields as applications of the theory."
Metrics, Connections and Gluing Theorems by Clifford Taubes Pdf
In this book, the author's goal is to provide an introduction to some of the analytic underpinnings for the geometry of anti-self duality in 4-dimensions. Anti-self duality is rather special to 4-dimensions and the imposition of this condition on curvatures of connections on vector bundles and on curvatures of Riemannian metrics has resulted in some spectacular mathematics. The book reviews some basic geometry, but is is assumed that the reader has a general background in differential geometry (as would be obtained by reading a standard text on the subject). Some of the fundamental references include Atiyah, Hitchin and Singer, Freed and Uhlenbeck, Donaldson and Kronheimer, and Kronheimer and Mrowka. The last chapter contains open problems and conjectures.
Bundles, connections, metrics and curvature are the lingua franca of modern differential geometry and theoretical physics. Supplying graduate students in mathematics or theoretical physics with the fundamentals of these objects, this book would suit a one-semester course on the subject of bundles and the associated geometry.
Differential Geometry by Jesús A. Alvarez López,Eduardo García-Río Pdf
A brief portrait of the life and work of Professor Enrique Vidal Abascal / L.A. Cordero -- pt. A. Foliation theory. Characteristic classes for Riemannian foliations / S. Hurder. Non unique-ergodicity of harmonic measures: Smoothing Samuel Petite's examples / B, Deroin. On the uniform simplicity of diffeomorphism groups / T. Tsuboi. On Bennequin's isotopy lemma and Thurston's inequality / Y. Mitsumatsu. On the Julia sets of complex codimension-one transversally holomorphic foliations / T. Asuke. Singular Riemannian foliations on spaces without conjugate points / A. Lytchak. Variational formulae for the total mean curvatures of a codimension-one distribution / V. Rovenski and P. Walczak. On a Weitzenböck-like formula for Riemannian foliations / V. Slesar. Duality and minimality for Riemannian foliations on open manifolds / X.M. Masa. Open problems on foliations -- pt. B. Riemannian geometry. Graphs with prescribed mean curvature / M. Dajczer. Genuine isometric and conformal deformations of submanifolds / R. Tojeiro. Totally geodesic submanifolds in Riemannian symmetric spaces / S. Klein. The orbits of cohomogeneity one actions on complex hyperbolic spaces / J.C. Díaz-Ramos. Rigidity results for geodesic spheres in space forms / J. Roth. Mean curvature flow and Bernstein-Calabi results for spacelike graphs / G. Li and I.M.C. Salavessa. Riemannian geometric realizations for Ricci tensors of generalized algebraic curvature operators / P. Gilkey, S. Nikc̮ević and D. Westerman. Conformally Osserman multiply warped product structures in the Riemannian setting / M. Brozos-Vázquez, M.E. Vázquez-Abal and R. Vázquez-Lorenzo. Riemannian [symbol]-symmetric spaces / M. Goze and E. Remm. Methods for solving the Jacobi equation. Constant osculating rank vs. constant Jacobi osculating rank / T. Arias-Marco. On the reparametrization of affine homogeneous geodesics / Z. Dus̮ek. Conjugate connections and differential equations on infinite dimensional manifolds / M. Aghasi [und weitere]. Totally biharmonic submanifolds / D. Impera and S. Montaldo. The biharmonicity of unit vector fields on the Poincaré half-space H[symbol] / M.K. Markellos. Perspectives on biharmonic maps and submanifolds / A. Balmus. Contact pair structures and associated metrics / G. Bande and A. Hadjar. Paraquaternionic manifolds and mixed 3-structures / S. Ianus and G.E. Vi̮lcu. On topological obstruction of compact positively Ricci curved manifolds / W.-H. Chen. Gray curvature conditions and the Tanaka-Webster connection / R. Mocanu. Riemannian structures on higher order frame bundles from classical linear connections / J. Kurek and W.M. Mikulski. Distributions on the cotangent bundle from torsion-free connections / J. Kurek and W.M. Mikulski. On the geodesics of the rotational surfaces in the Bianchi-Cartan-Vranceanu spaces / P. Piu and M.M. Profir. Cotangent bundles with general natural Kähler structures of quasi-constant holomorphic sectional curvatures / S.L. Druta̮. Polynomial translation Weingarten surfaces in 3-dimensional Euclidean space / M.I. Munteanu and A.I. Nistor. G-structures defined on pseudo-Riemannian manifolds / I. Sánchez-Rodríguez -- List of participants
New Horizons In Differential Geometry And Its Related Fields by Toshiaki Adachi,Hideya Hashimoto Pdf
This volume presents recent developments in geometric structures on Riemannian manifolds and their discretizations. With chapters written by recognized experts, these discussions focus on contact structures, Kähler structures, fiber bundle structures and Einstein metrics. It also contains works on the geometric approach on coding theory.For researchers and students, this volume forms an invaluable source to learn about these subjects that are not only in the field of differential geometry but also in other wide related areas. It promotes and deepens the study of geometric structures.
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.
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.
A Course in Metric Geometry by Dmitri Burago,Yuri Burago,Sergei Ivanov Pdf
“Metric geometry” is an approach to geometry based on the notion of length on a topological space. This approach experienced a very fast development in the last few decades and penetrated into many other mathematical disciplines, such as group theory, dynamical systems, and partial differential equations. The objective of this graduate textbook is twofold: to give a detailed exposition of basic notions and techniques used in the theory of length spaces, and, more generally, to offer an elementary introduction into a broad variety of geometrical topics related to the notion of distance, including Riemannian and Carnot-Carathéodory metrics, the hyperbolic plane, distance-volume inequalities, asymptotic geometry (large scale, coarse), Gromov hyperbolic spaces, convergence of metric spaces, and Alexandrov spaces (non-positively and non-negatively curved spaces). The authors tend to work with “easy-to-touch” mathematical objects using “easy-to-visualize” methods. The authors set a challenging goal of making the core parts of the book accessible to first-year graduate students. Most new concepts and methods are introduced and illustrated using simplest cases and avoiding technicalities. The book contains many exercises, which form a vital part of the exposition.