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Riemannian Manifolds

  • Amiya Mukherjee

Abstract

The metric on a manifoldM that we considered so far comes from Smirnov’s theorem (see Theorem 2.1.5), and also from the fact that M is embeddable in some Euclidean space. Of these, the second metric is more important for us, because the first metric has nothing to do with smooth structure, it may be obtained for any nice topological manifold. In this chapter we shall obtain another metric on M which gives the same topology of M as a manifold.

Keywords

RIEMANNIAN Manifold Tangent Vector Open Neighbourhood Smooth Curve Smooth Vector 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Hindustan Book Agency 2015

Authors and Affiliations

  • Amiya Mukherjee
    • 1
  1. 1.Statistics and Mathematics UnitIndian Statistical InstituteCalcuttaIndia

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