Chapter II

Differentiable Manifolds


Topological spaces; Hausdorff spaces; Compact and paracompact spaces; Continuity of mappings between topological spaces; Partition of unity; Connected spaces; Metric spaces; Normed spaces; Inner product spaces; Differentiable manifolds; Charts and atlases; Submersion; Immersion; Embedding; Submanifolds; Tangent vectors; Tangent spaces; Differential of a mapping: Tangent bundle; Vector fields; Flows; Lie derivative; Lie algebra; Distributions; Involutive distributions; Frobenius' theorem

2.1 Scope of the Chapter

The concept of manifold is essentially propounded to extend the definition of surfaces in classical differential geometry to higher dimensional spaces. This relatively new concept was first introduced ...

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