On hypersurfaces in a Riemannian vector bundle with prescribed Gaussian curvature and convexity |
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Authors: | Email author" target="_blank">Abdellah?HananiEmail author |
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Institution: | (1) Université des Sciences et Technologies de Lille, UFR de Mathématiques, Bât. M2, 59655 Villeneuve d Ascq Cedex, France |
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Abstract: | Let M be a compact Riemannian manifold, E a Riemannian vector bundle on M and the unit subbundle of E. We prove that there is no radial graph on with a strictly positive Gaussian curvature and that the Gaussian curvature of a convex radial graph must be identically equal to zero. Moreover, by solving on a nonlinear degenerate equation of Monge-Ampère type, we prove the existence of radial graphs having simultaneously a Gaussian curvature identically equal to zero and a prescribed strictly positive vertical Gaussian curvature.Mathematics Subject Classification (2000):35J60, 53C55, 58G30 |
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