Isometric immersions into Sn x R and Hn x R and applications to minimal surfaces
Abstract
We give a necessary and sufficient condition for an n-dimensional Riemannian manifold to be isometrically immersed in Sn x R or Hn 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 S2 x R or H2 x R, obtained by rotating the shape operator.
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