Geometric Structures On Manifolds
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Author |
: Сергей Петрович Новиков |
Publisher |
: American Mathematical Soc. |
Total Pages |
: 658 |
Release |
: 2006 |
ISBN-10 |
: 9780821839294 |
ISBN-13 |
: 0821839292 |
Rating |
: 4/5 (94 Downloads) |
Synopsis Modern Geometric Structures and Fields by : Сергей Петрович Новиков
Presents 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 |
: Krzysztof Galicki |
Publisher |
: Springer Science & Business Media |
Total Pages |
: 303 |
Release |
: 2010-07-25 |
ISBN-10 |
: 9780817647438 |
ISBN-13 |
: 0817647430 |
Rating |
: 4/5 (38 Downloads) |
Synopsis Riemannian Topology and Geometric Structures on Manifolds by : Krzysztof Galicki
Riemannian 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 |
: William M. Goldman |
Publisher |
: American Mathematical Society |
Total Pages |
: 494 |
Release |
: 2022-12-20 |
ISBN-10 |
: 9781470471989 |
ISBN-13 |
: 1470471981 |
Rating |
: 4/5 (89 Downloads) |
Synopsis Geometric Structures on Manifolds by : William M. Goldman
The theory of geometric structures on manifolds which are locally modeled on a homogeneous space of a Lie group traces back to Charles Ehresmann in the 1930s, although many examples had been studied previously. Such locally homogeneous geometric structures are special cases of Cartan connections where the associated curvature vanishes. This theory received a big boost in the 1970s when W. Thurston put his geometrization program for 3-manifolds in this context. The subject of this book is more ambitious in scope. Unlike Thurston's eight 3-dimensional geometries, it covers structures which are not metric structures, such as affine and projective structures. This book describes the known examples in dimensions one, two and three. Each geometry has its own special features, which provide special tools in its study. Emphasis is given to the interrelationships between different geometries and how one kind of geometric structure induces structures modeled on a different geometry. Up to now, much of the literature has been somewhat inaccessible and the book collects many of the pieces into one unified work. This book focuses on several successful classification problems. Namely, fix a geometry in the sense of Klein and a topological manifold. Then the different ways of locally putting the geometry on the manifold lead to a “moduli space”. Often the moduli space carries a rich geometry of its own reflecting the model geometry. The book is self-contained and accessible to students who have taken first-year graduate courses in topology, smooth manifolds, differential geometry and Lie groups.
Author |
: Danny Calegari |
Publisher |
: Oxford University Press on Demand |
Total Pages |
: 378 |
Release |
: 2007-05-17 |
ISBN-10 |
: 9780198570080 |
ISBN-13 |
: 0198570082 |
Rating |
: 4/5 (80 Downloads) |
Synopsis Foliations and the Geometry of 3-Manifolds by : Danny Calegari
This unique reference, aimed at research topologists, gives an exposition of the 'pseudo-Anosov' theory of foliations of 3-manifolds. This theory generalizes Thurston's theory of surface automorphisms and reveals an intimate connection between dynamics, geometry and topology in 3 dimensions. Significant themes returned to throughout the text include the importance of geometry, especially the hyperbolic geometry of surfaces, the importance of monotonicity, especially in1-dimensional and co-dimensional dynamics, and combinatorial approximation, using finite combinatorical objects such as train-tracks, branched surfaces and hierarchies to carry more complicated continuous objects.
Author |
: R.B. Sher |
Publisher |
: Elsevier |
Total Pages |
: 1145 |
Release |
: 2001-12-20 |
ISBN-10 |
: 9780080532851 |
ISBN-13 |
: 0080532853 |
Rating |
: 4/5 (51 Downloads) |
Synopsis Handbook of Geometric Topology by : R.B. Sher
Geometric Topology is a foundational component of modern mathematics, involving the study of spacial properties and invariants of familiar objects such as manifolds and complexes. This volume, which is intended both as an introduction to the subject and as a wide ranging resouce for those already grounded in it, consists of 21 expository surveys written by leading experts and covering active areas of current research. They provide the reader with an up-to-date overview of this flourishing branch of mathematics.
Author |
: Frank Nielsen |
Publisher |
: Springer |
Total Pages |
: 395 |
Release |
: 2018-11-19 |
ISBN-10 |
: 9783030025205 |
ISBN-13 |
: 3030025209 |
Rating |
: 4/5 (05 Downloads) |
Synopsis Geometric Structures of Information by : Frank Nielsen
This book focuses on information geometry manifolds of structured data/information and their advanced applications featuring new and fruitful interactions between several branches of science: information science, mathematics and physics. It addresses interrelations between different mathematical domains like shape spaces, probability/optimization & algorithms on manifolds, relational and discrete metric spaces, computational and Hessian information geometry, algebraic/infinite dimensional/Banach information manifolds, divergence geometry, tensor-valued morphology, optimal transport theory, manifold & topology learning, and applications like geometries of audio-processing, inverse problems and signal processing. The book collects the most important contributions to the conference GSI’2017 – Geometric Science of Information.
Author |
: Masahiro Kon |
Publisher |
: World Scientific |
Total Pages |
: 520 |
Release |
: 1985-02-01 |
ISBN-10 |
: 9789814602808 |
ISBN-13 |
: 9814602809 |
Rating |
: 4/5 (08 Downloads) |
Synopsis Structures On Manifolds by : Masahiro Kon
Contents: Riemannian ManifoldsSubmanifolds of Riemannian ManifoldsComplex ManifoldsSubmanifolds of Kaehlerian ManifoldsContact ManifoldsSubmanifolds of Sasakian Manifoldsf-StructuresProduct ManifoldsSubmersions Readership: Mathematicians. Keywords:Riemannian Manifold;Submanifold;Complex Manifold;Contact Manifold;Kaehlerian Manifold;Sasakian Manifold;Anti-Invariant Submanifold;CR Submanifold;Contact CR Submanifold;Submersion
Author |
: Walter A. Poor |
Publisher |
: Courier Corporation |
Total Pages |
: 356 |
Release |
: 2015-04-27 |
ISBN-10 |
: 9780486151915 |
ISBN-13 |
: 0486151913 |
Rating |
: 4/5 (15 Downloads) |
Synopsis Differential Geometric Structures by : Walter A. Poor
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.
Author |
: Vicente Muñoz |
Publisher |
: American Mathematical Soc. |
Total Pages |
: 408 |
Release |
: 2020-10-21 |
ISBN-10 |
: 9781470461324 |
ISBN-13 |
: 1470461323 |
Rating |
: 4/5 (24 Downloads) |
Synopsis Geometry and Topology of Manifolds: Surfaces and Beyond by : Vicente Muñoz
This book represents a novel approach to differential topology. Its main focus is to give a comprehensive introduction to the classification of manifolds, with special attention paid to the case of surfaces, for which the book provides a complete classification from many points of view: topological, smooth, constant curvature, complex, and conformal. Each chapter briefly revisits basic results usually known to graduate students from an alternative perspective, focusing on surfaces. We provide full proofs of some remarkable results that sometimes are missed in basic courses (e.g., the construction of triangulations on surfaces, the classification of surfaces, the Gauss-Bonnet theorem, the degree-genus formula for complex plane curves, the existence of constant curvature metrics on conformal surfaces), and we give hints to questions about higher dimensional manifolds. Many examples and remarks are scattered through the book. Each chapter ends with an exhaustive collection of problems and a list of topics for further study. The book is primarily addressed to graduate students who did take standard introductory courses on algebraic topology, differential and Riemannian geometry, or algebraic geometry, but have not seen their deep interconnections, which permeate a modern approach to geometry and topology of manifolds.
Author |
: Aurel Bejancu |
Publisher |
: Springer Science & Business Media |
Total Pages |
: 309 |
Release |
: 2006-01-17 |
ISBN-10 |
: 9781402037207 |
ISBN-13 |
: 1402037201 |
Rating |
: 4/5 (07 Downloads) |
Synopsis Foliations and Geometric Structures by : Aurel Bejancu
Offers 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.