Notes On Differentiable Geometry

Basically, manifolds are geometrical objects or abstract sets which are endowed with coordinates, so that using these coordinates one can apply differential and integral calculus. Examples of manifolds may be seen as open domains in Euclidean space, and include multi-dimensional surfaces such as the n- sphere and n- torus, the projective spaces, and their generalizations, matrix groups such as the rotation group SO(n),etc. Differentiable manifolds naturally appear in various applications such as configuration spaces in mechanics. Differentiable manifolds are arguably the most general objects where calculus can be developed. On the other hand, they provide a very powerful invariant geometric language for calculus, which is universally used now a days. "Notes On Differentiable Geometry" discusses the theory of various structures on manifolds and their submanifolds. Lucid explanation of the concepts will definitely serve the purpose for which it is meant. The book will surely enrich the researchers working in the field of differential geometry, specially for those, who are interested in the study of structures on differentiable manifolds.