A fundamental differential system of 3-dimensional Riemannian geometry

Rui Albuquerque

doi:10.1016/j.bulsci.2018.01.001

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arXiv · 1504.04659

A fundamental differential system of 3-dimensional Riemannian geometry

Rui Albuquerque

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Abstract

We briefly recall a fundamental exterior differential system introduced by the author and then apply it to the case of three dimensions. Here we find new global tensors and intrinsic invariants of oriented Riemaniann 3-manifolds. The system leads to a remarkable Weingarten type equation for surfaces on hyperbolic 3-space. An independent proof for low dimensions of the structural equations gives new insight on the intrinsic exterior differential system.

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BibTeX RIS

Rui Albuquerque. 2015-04-17. A fundamental differential system of 3-dimensional Riemannian geometry. https://doi.org/10.1016/j.bulsci.2018.01.001

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