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

Autor:	Hanani, Abdellah
Rok vydání:	2016
Předmět:	Mathematics - Differential Geometry 35J60 53C55 58G30
Druh dokumentu:	Working Paper
Popis:	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-Amp\`ere type. Comment: 30 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1601.06632 Zobrazit plný text záznamu View this record from Arxiv