Isometric immersions into ⁿ×ℝ and ℍⁿ×ℝ and applications to minimal surfaces

By Benoît Daniel. 2009

67 citations recorded by the source corpus.

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 × 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 × ℝ or ℍ 2 x R, obtained by rotating the shape operator.

Subfields: Applied Mathematics, Astronomy and Astrophysics, Cell Biology

View Paper: https://www.semanticscholar.org/paper/d88afa6c8fd9940d78775325358184369718f067

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

1. L. Hauswirth
2. Benoît Daniel
3. Ricardo Sa Earp
4. Eric Toubiana
5. I. Fernández
6. Pablo Mira
7. Rabah Souam
8. H. Rosenberg

In Astronomy and Astrophysics

1. L. Hauswirth
2. I. Fernández
3. Pablo Mira
4. Rabah Souam
5. Eric Toubiana
6. Iskander A. Taimanov
7. Dmitry Berdinsky

In Cell Biology

1. L. Hauswirth
2. Ricardo Sa Earp

Citations in the corpus

• Half‐space theorem, embedded minimal annuli and minimal graphs in the Heisenberg group (2007, background): “In [ 6 , 15], it is proved that the conjugate immersion exists.”