Revista Matemática Iberoamericana

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Volume 35, Issue 7, 2019, pp. 2221–2250
DOI: 10.4171/rmi/1118

Published online: 2019-07-22

A fundamental differential system of Riemannian geometry

Rui Albuquerque[1]

(1) Universidade de Évora, Portugal

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.

Keywords: Tangent sphere bundle, Riemannian manifold, exterior differential system, hypersurface, Euler–Lagrange system

Albuquerque Rui: A fundamental differential system of Riemannian geometry. Rev. Mat. Iberoam. 35 (2019), 2221-2250. doi: 10.4171/rmi/1118