Displaying similar documents to “Submanifold geometry and Hessians on the pseudoriemannian manifold of metrics.”

Integral formulae for a Riemannian manifold with two orthogonal distributions

Vladimir Rovenski (2011)

Open Mathematics

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We obtain a series of new integral formulae for a distribution of arbitrary codimension (and its orthogonal complement) given on a closed Riemannian manifold, which start from the formula by Walczak (1990) and generalize ones for foliations by several authors. For foliations on space forms our formulae reduce to the classical type formulae by Brito-Langevin-Rosenberg (1981) and Brito-Naveira (2000). The integral formulae involve the conullity tensor of a distribution, and certain components...

Infinitesimal conjugacies and Weil-Petersson metric

Albert Fathi, L. Flaminio (1993)

Annales de l'institut Fourier

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We study deformations of compact Riemannian manifolds of negative curvature. We give an equation for the infinitesimal conjugacy between geodesic flows. This in turn allows us to compute derivatives of intersection of metrics. As a consequence we obtain a proof of a theorem of Wolpert.

A spectral estimate for the Dirac operator on Riemannian flows

Nicolas Ginoux, Georges Habib (2010)

Open Mathematics

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We give a new upper bound for the smallest eigenvalues of the Dirac operator on a Riemannian flow carrying transversal Killing spinors. We derive an estimate on both Sasakian and 3-dimensional manifolds, and partially classify those satisfying the limiting case. Finally, we compare our estimate with a lower bound in terms of a natural tensor depending on the eigenspinor.