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

Benoit Daniel

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arXiv · math/0406426

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

Benoit Daniel

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Abstract

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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Benoit Daniel. 2004-06-22. Isometric immersions into S^n x R and H^n x R and applications to minimal surfaces. https://arxiv.org/abs/math/0406426

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