TY  - GEN
AU  - Kumaresan,S
TI  - A Course in differential geometry and lie groups
T2  - Texts and Readings in Mathematics
SN  - 9788185931678
U1  - 516.36 23rd
PY  - 2017///
CY  - New Delhi
PB  - HBA
KW  - Mathematics
KW  - Differential Geometry
KW  - Differential Manifolds
KW  - Riemannian Geometry
N1  - Differential Calculus -- manifolds and lie groups -- Tensor analysis -- Integration -- Riemannian geometry
N2  - This book covers the traditional topics of differential manifolds, tensor fields, Lie groups, integration on manifolds and basic differential and Riemannian geometry. The author emphasizes geometric concepts, giving the reader a working knowledge of the topic. Motivations are given, exercises are included, and illuminating nontrivial examples are discussed. Important features include the following: Geometric and conceptual treatment of differential calculus with a wealth of nontrivial examples. A thorough discussion of the much-used result on the existence, uniqueness, and smooth dependence of solutions of ODEs. Careful introduction of the concept of tangent spaces to a manifold. Early and simultaneous treatment of Lie groups and related concepts. A motivated and highly geometric proof of the Frobenius theorem. A constant reconciliation with the classical treatment and the modern approach. Simple proofs of the hairy-ball theorem and Brouwer's fixed point theorem. Construction of manifolds of constant curvature a la Chern. This text would be suitable for use as a graduate-level introduction to basic differential and Riemannian geometry
ER  -