Classification of constant angle hypersurfaces in warped products via eikonal functions

Details Classification of constant angle hypersurfaces in warped products via eikonal functions Classification of constant angle hypersurfaces in warped products via eikonal functions

2011-03-31

arxiv.org/abs/1104.0050v3

Mathematics

Differential Geometry

16 pages

Scientific paper

Given a warped product of the real line with a Riemannian manifold of arbitrary dimension, we classify the hypersurfaces whose tangent spaces make a constant angle with the vector field tangent to the real direction. We show that this is a natural setting in which to extend previous results in this direction made by several authors. Moreover, when the constant angle hypersurface is a graph over the Riemannian manifold, we show that the function involved satisfies a generalized eikonal equation, which we solve via a geometric method. In the final part of this paper we prove that minimal constant angle hypersurfaces are cylinders over minimal submanifolds.

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