DIFFERENTIAL GEOMETRY OF MANIFOLDS----------PHI
Description:
Curves and
surfaces are objects that everyone can see, and many of the questions
that can be asked about them are natural and easily understood.
Differential geometry is concerned with the precise mathematical
formulation of some of these questions, while trying to answer them
using calculus techniques. The geometry of differentiable manifolds with
structures is one of the most important branches of modern differential
geometry.
This well-written book discusses the theory of differential and
Riemannian manifolds to help students understand the basic structures
and consequent developments. While introducing concepts such as bundles,
exterior algebra and calculus, Lie group and its algebra and calculus,
Riemannian geometry, submanifolds and hypersurfaces, almost complex
manifolds, etc., enough care has been taken to provide necessary details
which enable the reader to grasp them easily. The material of this book
has been successfully tried in classroom teaching.
The book is designed for the postgraduate students of Mathematics. It
will also be useful to the researchers working in the field of
differential geometry and its applications to general theory of
relativity and cosmology, and other applied areas.
KEY FEATURES
Provides basic concepts in an easy-to-understand style.
Presents the subject in a natural way.
Follows a coordinate-free approach.
Includes a large number of solved examples and illuminating illustrations.
Gives notes and remarks at appropriate places.
Contents:
Preface
1. PRELIMINARIES
2. DIFFERENTIABLE MANIFOLDS
3. DIFFERENTIAL FORMS, BUNDLES, LIE GROUPS AND LIE ALGEBRAS
4. RIEMANNIAN MANIFOLDS
5. SUBMANIFOLDS AND HYPERSURFACES
6. ALMOST COMPLEX MANIFOLDS
Bibliography
Index
