Notes on Differentiable Manifolds

The book comprises of two parts: The first part (having 10 Chapters) includes a brief discussion of pre-requites such as: Number System; (ii) Plain (Euclidean) geometry, (iii) Matrices, (iv) Algebraic Structures (Sets and Functions, Groups, Rings, Fields, Integral domains); (v) Linear (or Vector) spaces, (vi) Metric spaces, (vii) Topological spaces, and (viii) Linear Algebra. Part 2 consists of the five chapters: of which the Chapter 11 deals with the theory of manifolds. It covers the basic concepts, type of manifolds, their various aspects: topological, symplectic, differentiability etc. are covered. Kähler manifolds are introduced in the Chapter 12, which also includes a discussion of Sasakian manifolds. Theory of ‘Tangent Bundles and Vector Bundles’ is presented in Chapter 13. It includes the Tensor Bundles too. Contact Manifolds are presented in the next chapter while the Tachibana and Otsuki spaces form the subject matter of the last chapter. Certain concepts such as Charts, Atlas, Projections, Tangent Surface, Vector Bundles, Contact Manifolds, etc. ever hunt the minds of explorers. The authors feel contended to have humbly presented the topics in the manner easy to comprehend. The subject being of advanced level its study requires the knowledge of Algebra, Linear Algebra, Differential Geometry, Topology and alike. The course contents may best suit graduate and postgraduate programmes of any University and can be covered in one semester with 3 credit hours per week.