JournalsrmiVol. 35, No. 7pp. 2221–2250

A fundamental differential system of Riemannian geometry

  • Rui Albuquerque

    Universidade de Évora, Portugal
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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 nn associated to any given oriented Riemannian manifold MM of dimension n+1n + 1. The framework is that of the tangent sphere bundle of MM. 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.

Cite this article

Rui Albuquerque, A fundamental differential system of Riemannian geometry. Rev. Mat. Iberoam. 35 (2019), no. 7, pp. 2221–2250

DOI 10.4171/RMI/1118