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We discover a fundamental exterior differential system of Riemannian geometry; indeed, an intrinsic and invariant global system of differential forms of degree associated to any given oriented Riemannian manifold of dimension . The framework is that of the tangent sphere bundle of . 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, A fundamental differential system of Riemannian geometry. Rev. Mat. Iberoam. 35 (2019), no. 7, pp. 2221–2250DOI 10.4171/RMI/1118