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Pré-Publication, Document De Travail Année : 2018

A local Blaschke-Petkantschin formula in a Riemannian manifold

Résumé

In this paper, we show a local Blaschke-Petkantschin formula for a Riemannian manifold. Namely, we compute the Jacobian determinant of the parametrization of (n + 1)-tuples of the manifold by the center and the radius of their common circumscribed sphere as well as the (n + 1) directions characterizing the positions of the n + 1 points on it. We deduce from it a more explicit two-term expansion when the radius tends to 0. This formula contains a local correction with respect to the flat case which involves the Ricci curvatures in the (n + 1) directions.
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Dates et versions

hal-01847049 , version 1 (23-07-2018)

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  • HAL Id : hal-01847049 , version 1

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Aurélie Chapron. A local Blaschke-Petkantschin formula in a Riemannian manifold. 2018. ⟨hal-01847049⟩
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