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关键词：
Differential Geometry of Manifolds
书目信息
ISBN：
9781842653715（13位）
中图分类号：
O1
杜威分类号：
中文译名：
Manifolds微分几何
作者：
U. C. De, A. A. Shaikh
编者：
语种：
English
出版信息
出版社：
Alpha Science International Limited
出版地：
出版年：
2006
版本：
版本类型：
原版
丛书题名：
卷期：
文献信息
关键词：
Mathematics
前言：
摘要：
内容简介：
In this text the authors have compiled all the basic topics and important concepts regarding differentiable Manifolds and different structures thereon. The primary aim is to cover the syllabi of different Indian Universities following the model U.G.C. curriculum. This book will also benefit researchers in the field of differential geometry and its applications in relativity theory, statistics, cosmology and biomathematics etc.
目次：
Some Preliminaries: Metric Spaces / Topological Spaces / Linear Algebra / Differentiable Manifolds: Definition and Examples of Differentiable Manifolds / Differentiable Functions on a Manifold / Tangent Spaces / Vector Fields on Differentiable Manifolds / Integral Curves and Flows / One Parameter Group of Transformations of a Manifold / Exterior Algebra and Exterior Derivative: Tensor Product / Tensor Algebra / Exterior Algebra / Exterior Derivative / Lie Group and Lie Algebras: Definition and Examples of Lie Groups / The Lie Algebra of a Lie Group / Lie Groups Homomorphism and Isomorphism / One Parameter Subgroup and Exponential Map / Lie Transformation Groups / Lei Derivative / Fibre Bundles: Principal Fibre Bundle / Linear Frame Bundle / Associated Principal Bundle / Vector Bundles / Bundle Homomorphism / Tangent Bundle / Linear Connections: Definition and Examples of Affine Connection / Torsion Tensor of an Affine Connection / Geodesic Normal Coordinates / Curvature Tensor of an Affine Connection / Riemannian Manifolds: Definition and Examples of Riemannian Manifolds / Riemannian Connection / Fundamental Theorem of Riemannian Geometry / Riemannian Curvature Tensor / Bianchi Identities / Ricci Identity / Ricci Tensor and Scalar Curvature / Geodesic of a Riemannian Manifold / Riemannian Manifold as a Metric Space / Gradient Vector Fields / Semi-symmetric Metric Connection / Sectional Curvatures / Schur’s Theorem / Riemannian Manifold of Constant Curvature / Einstein Manifolds / Conformal, Concircular, Projective, Conharmonic Curvature Tensors / Locally Symmetric and semi-symmetric Riemannian Manifolds / Submanifolds: Submanifolds of a Riemannian Manifold / Induced Connection and Second Fundamental Form / Equations of Gauss-Codazzi and Ricci / Mean Curvature / Complex Manifold: Algebraic Preliminaries / Almost Complex Structure / Nijenhuis Tensor / Almost Hermite Manifold / K?hler Manifold / Almost Tachibana Manifold / Almost Product and Almost Decomposable Manifold / F-connection.
附录：
全文链接：
读者对象：
Undergraduate – Postgraduate Students in Mathematics
实体信息
页码：
350
装帧：
Hardback
尺寸：
其它形态细节：
其它信息
原价：
GBP
29.9500
原版ISBN：
其它ISBN：
图书特色：
书评：
扩展信息
Isbn：
1842653717
issue：
2006JC02
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