On compact hypersurfaces in a Riemannian vector bundle with prescribed vertical Gaussian curvature

Abdellah Hanani

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arXiv · 1601.06632

On compact hypersurfaces in a Riemannian vector bundle with prescribed vertical Gaussian curvature

Abdellah Hanani

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Abstract

Let M be a compact Riemannian manifold and E a Riemannian vector bundle on M. We look for hypersurfaces of E with a prescribed vertical Gaussian curvature. In trying to solve this problem fibre-wise, we loose the regularity of the resulting solution. To unsure the smoothness of the solution, we construct it as a radial graph over the unit sphere subbundle of E and prove its existence by solving in this one a nonlinear partial differential equation of Monge-Ampère type.

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Abdellah Hanani. 2016-01-25. On compact hypersurfaces in a Riemannian vector bundle with prescribed vertical Gaussian curvature. https://arxiv.org/abs/1601.06632

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