Isometric immersions into S^n x R and H^n x R and applications to minimal surfaces

Details Isometric immersions into S^n x R and H^n x R and applications to minimal surfaces Isometric immersions into S^n x R and H^n x R and applications to minimal surfaces

2004-06-22

arxiv.org/abs/math/0406426v1

Trans. Amer. Math. Soc. 361 (2009), no. 12, 6255-6282

Mathematics

Differential Geometry

27 pages, 1 figure

Scientific paper

We give a necessary and sufficient condition for an n-dimensional Riemannian manifold to be isometrically immersed in S^n x R or H^n x R in terms of its first and second fundamental forms and of the projection of the vertical vector field on its tangent plane. We deduce the existence of a one-parameter family of isometric minimal deformations of a given minimal surface in S^2 x R or H^2 x R, obtained by rotating the shape operator.

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