Introduction to Riemannian Manifolds

  title={Introduction to Riemannian Manifolds},
  author={Mircea Craioveanu and Mircea Puta and Themistocles M. Rassias},
Let M (resp. N) be a connected. smooth (= C x ) n-dimensional manifold without boundary. We denote by C x (M) the ring of smooth real valued functions on M and by x(M) the Lie-algebra of all smooth vector fields on M. Recall that X ∈ x(M) is a smooth map $$X:M \to TM = \mathop U\limits_{x \in M} {T_x}M$$ such that X (x) = X x , ∈ T x M (= the tangent space of Mat x) for each x ∈ M. T x M may be characterized as the space of all derivations of the algebra of smooth real valued functions… 

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