Isometric immersions into S n ×R and H n ×R and applications to minimal surfaces
نویسنده
چکیده
We give a necessary and sufficient condition for an n-dimensional Riemannian manifold to be isometrically immersed in Sn×R or Hn×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 ×R or H × R, obtained by rotating the shape operator.
منابع مشابه
Isometric Immersions into S × R and H × R and Applications to Minimal Surfaces
We give a necessary and sufficient condition for an n-dimensional Riemannian manifold to be isometrically immersed in Sn×R or Hn×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 ×R or H2 × R, obtained by...
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