A fundamental differential system of Riemannian geometry

Abstract

We discover a fundamental exterior differential system of Riemannian geometry; indeed, an intrinsic and invariant global system of differential forms of degree $n$ associated to any given oriented Riemannian manifold $M$ of dimension $n+1$. The framework is that of the tangent sphere bundle of $M$. We generalise to a Riemannian setting some results from the theory of hypersurfaces in flat Euclidean space. We give new applications and examples of the associated Euler-Lagrange differential systems.

Final version, very close to the one published; 32 pp

References in corpus (6)

• 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
• A fundamental differential system of 3-dimensional Riemannian geometry
• Curvatures of weighted metrics on tangent sphere bundles

Cited by in corpus (5)

• Notes on the Sasaki metric
• On the volume of a unit vector field in 3 dimensions via calibrations
• The volume of a unit vector field in 2 dimensions via calibrations
• New Hsiung-Minkowski identities
• The Euler characteristic of hypersurfaces in space forms and applications to isoparametric hypersurfaces