A fundamental differential system of Riemannian geometry

Rui Albuquerque

doi:10.4171/rmi/1118

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arXiv · 1112.3213

A fundamental differential system of Riemannian geometry

Rui Albuquerque

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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.

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Rui Albuquerque. 2011-12-14. A fundamental differential system of Riemannian geometry. https://doi.org/10.4171/rmi%2F1118

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