m p do carmo riemannian geometry pdf

They can, therefore, be transported to a regular surface, without further difficulties, as follows. Assume now that x is bijective. Murtala Yusuf. Furthermore, at a nonplanar umbilic, every orthogonal pair of directions is a pair of conjugate directions, and at a planar umbilic each direction is conjugate to any other direction. A computation entirely similar to the one made to obtain Eq.

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