ISOMETRIC IMMERSIONS INTO LORENTZIAN PRODUCTS-Reference-Cited by-同舟云学术

ISOMETRIC IMMERSIONS INTO LORENTZIAN PRODUCTS

Published:2011-09 Issue:06 Volume:08 Page:1269-1290
ISSN:0219-8878
Container-title:International Journal of Geometric Methods in Modern Physics
language:en
Short-container-title:Int. J. Geom. Methods Mod. Phys.

Author:

ROTH JULIEN¹

Affiliation:

1. LAMA, Université Paris-Est — Marne-la-Vallée, 5 Bd Descartes, Cité Descartes, Champs-sur-Marne, F-77454 Marne-la-Vallée, France

Abstract

We give a necessary and sufficient condition for an n-dimensional Riemannian manifold to be isometrically immersed into one of the Lorentzian products 𝕊n × ℝ1 or ℍn × ℝ1. This condition is expressed in terms of its first and second fundamental forms, the tangent and normal projections of the vertical vector field. As applications, we give an equivalent condition in a spinorial way and we deduce the existence of a one-parameter family of isometric maximal deformation of a given maximal surface obtained by rotating the shape operator.

Publisher

World Scientific Pub Co Pte Lt

Subject

Physics and Astronomy (miscellaneous)

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0219887811005695

Reference14 articles.

1. Generalized cylinders in semi-Riemannian and spin geometry

2. Teubner-Texte zur Mathematik, Band 41;Baum H.,1981

3. Codazzi spinors and globally hyperbolic manifolds with special holonomy

4. Riemannian Geometry

5. Isometric immersions into $\mathbb {S}^n\times \mathbb {R}$ and $\mathbb {H}^n\times \mathbb {R}$ and applications to minimal surfaces

Cited by 9 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. Spinorial Representation of Surfaces in Lorentzian Homogeneous Spaces of Dimension $$\varvec{3}$$;Advances in Applied Clifford Algebras;2022-02-21

2. A fundamental theorem for submanifolds in semi-Riemannian warped products;Journal of Geometry and Physics;2019-10

3. Associated Families of Surfaces in Warped Products and Homogeneous Spaces;Bulletin of the Belgian Mathematical Society - Simon Stevin;2019-09-01

4. A fundamental theorem for submanifolds of multiproducts of real space forms;Advances in Geometry;2017-07-01

5. Complex and Lagrangian surfaces of the complex projective plane via Kählerian Killing Spinc spinors;Journal of Geometry and Physics;2017-06