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Author: Walter A. Poor
Publisher: Courier Corporation
Published: 2015-04-27
Total Pages: 356
ISBN-13: 0486151913
DOWNLOAD EBOOKThis 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.
Author: Сергей Петрович Новиков
Publisher: American Mathematical Soc.
Published: 2006
Total Pages: 658
ISBN-13: 0821839292
DOWNLOAD EBOOKPresents the basics of Riemannian geometry in its modern form as geometry of differentiable manifolds and the important structures on them. This book shows that Riemannian geometry has a great influence to several fundamental areas of modern mathematics and its applications.
Author: Shoshichi Kobayashi
Publisher: Springer Science & Business Media
Published: 2012-12-06
Total Pages: 192
ISBN-13: 3642619819
DOWNLOAD EBOOKGiven 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.
Author: Jeffrey Marc Lee
Publisher: American Mathematical Soc.
Published: 2009
Total Pages: 690
ISBN-13: 0821848151
DOWNLOAD EBOOKDifferential geometry began as the study of curves and surfaces using the methods of calculus. This book offers a graduate-level introduction to the tools and structures of modern differential geometry. It includes the topics usually found in a course on differentiable manifolds, such as vector bundles, tensors, and de Rham cohomology.
Author: Toshiaki Adachi
Publisher: World Scientific
Published: 2022-04-07
Total Pages: 257
ISBN-13: 9811248117
DOWNLOAD EBOOKThis 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.
Author: Krzysztof Galicki
Publisher: Springer Science & Business Media
Published: 2010-07-25
Total Pages: 303
ISBN-13: 0817647430
DOWNLOAD EBOOKRiemannian Topology and Structures on Manifolds results from a similarly entitled conference held on the occasion of Charles P. Boyer’s 65th birthday. The various contributions to this volume discuss recent advances in the areas of positive sectional curvature, Kähler and Sasakian geometry, and their interrelation to mathematical physics, especially M and superstring theory. Focusing on these fundamental ideas, this collection presents review articles, original results, and open problems of interest.
Author: Aurel Bejancu
Publisher: Springer Science & Business Media
Published: 2006-01-17
Total Pages: 309
ISBN-13: 1402037201
DOWNLOAD EBOOKOffers basic material on distributions and foliations. This book introduces and builds the tools needed for studying the geometry of foliated manifolds. Its main theme is to investigate the interrelations between foliations of a manifold on the one hand, and the many geometric structures that the manifold may admit on the other hand.
Author: Norbert A'Campo
Publisher: Springer Nature
Published: 2021-10-27
Total Pages: 282
ISBN-13: 3030890325
DOWNLOAD EBOOKThis book provides an introduction to the main geometric structures that are carried by compact surfaces, with an emphasis on the classical theory of Riemann surfaces. It first covers the prerequisites, including the basics of differential forms, the Poincaré Lemma, the Morse Lemma, the classification of compact connected oriented surfaces, Stokes’ Theorem, fixed point theorems and rigidity theorems. There is also a novel presentation of planar hyperbolic geometry. Moving on to more advanced concepts, it covers topics such as Riemannian metrics, the isometric torsion-free connection on vector fields, the Ansatz of Koszul, the Gauss–Bonnet Theorem, and integrability. These concepts are then used for the study of Riemann surfaces. One of the focal points is the Uniformization Theorem for compact surfaces, an elementary proof of which is given via a property of the energy functional. Among numerous other results, there is also a proof of Chow’s Theorem on compact holomorphic submanifolds in complex projective spaces. Based on lecture courses given by the author, the book will be accessible to undergraduates and graduates interested in the analytic theory of Riemann surfaces.
Author: Gerard Walschap
Publisher: Springer Science & Business Media
Published: 2012-08-23
Total Pages: 235
ISBN-13: 0387218262
DOWNLOAD EBOOKThis 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.
Author: Christian Bär
Publisher: Springer Science & Business Media
Published: 2011-12-18
Total Pages: 520
ISBN-13: 3642228429
DOWNLOAD EBOOKThis volume contains a collection of well-written surveys provided by experts in Global Differential Geometry to give an overview over recent developments in Riemannian Geometry, Geometric Analysis and Symplectic Geometry. The papers are written for graduate students and researchers with a general interest in geometry, who want to get acquainted with the current trends in these central fields of modern mathematics.
