A fundamental differential system of 3-dimensional Riemannian geometry

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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References in corpus (5)

• Exterior Differential Systems and Euler-Lagrange Partial Differential Equations
• Homotheties and topology of tangent sphere bundles
• Weighted metrics on tangent sphere bundles
• Variations of gwistor space
• Curvatures of weighted metrics on tangent sphere bundles

Cited by in corpus (4)

• A fundamental differential system of Riemannian geometry
• Minkowski identities for hypersurfaces in constant sectional curvature manifolds
• On the volume of a unit vector field in 3 dimensions via calibrations
• The Euler characteristic of hypersurfaces in space forms and applications to isoparametric hypersurfaces