Isometric immersions into S^n x R and H^n x R and applications to minimal surfaces
By Benoît Daniel. 2004
97 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 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.
Subfields: Applied Mathematics, Biomedical Engineering, Cell Biology
View Paper: https://www.semanticscholar.org/paper/bd20365b43ac757b7ad3e2efd9a303cf73c601da
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In Applied Mathematics
- Ricardo Sa Earp
- Eric Toubiana
- L. Hauswirth
- Benoît Daniel
- H. Rosenberg
- I. Fernández
- Pablo Mira
- J. A. Gálvez
In Biomedical Engineering
In Cell Biology
Citations in the corpus
- Associate and conjugate minimal immersions in MxR (2005, methodology): “For related works on minimal surfaces in M × R , see for instance Daniel [4], Nelli and Rosenberg [12], Meeks and Rosenberg [11] and Rosenberg [13].”
- 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.”
- PARABOLIC AND HYPERBOLIC SCREW MOTION SURFACES IN ℍ2×ℝ (2008, methodology): “This formula has already been established by Benôıt Daniel [2] and this surface was known to Laurent Hauswirth [10].”