A fundamental differential system of 3-dimensional Riemannian geometry

@article{Albuquerque2018AFD,
  title={A fundamental differential system of 3-dimensional Riemannian geometry},
  author={R. Albuquerque},
  journal={Bulletin Des Sciences Mathematiques},
  year={2018},
  volume={143},
  pages={82-107}
}
  • R. Albuquerque
  • Published 2018
  • Mathematics
  • Bulletin Des Sciences Mathematiques
Abstract We briefly recall a fundamental exterior differential system of Riemannian geometry and apply it to the case of three dimensions. Here we find new global tensors and intrinsic invariants of oriented Riemannian 3-manifolds. In particular, we develop the study of ∇Ric. The exterior differential system leads to a remarkable Weingarten type equation for immersed surfaces in hyperbolic 3-space. A new independent proof for low dimensions of the structural equations gives new insight on the… Expand
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