Spinorial representation of submanifolds in metric Lie groups

JOURNAL OF GEOMETRY AND PHYSICS

卷:114

Article

Bayard, Pierre¹  Roth, Julien²  Jimenez, Berenice Zavala¹ 

[1] Univ Nacl Autonoma Mexico, Fac Ciencias, Mexico City 04510, DF, Mexico

[2] Univ Paris Est Marne La Vallee, Lab Anal & Math Appl, Champs Sur Marne, France

关键词: Spin geometry;    Metric Lie groups;    Isometric immersions;    Weierstrass representation;   

DOI  :  10.1016/j.geomphys.2016.12.011

来源: Elsevier

【 摘 要 】

In this paper we give a spinorial representation of submanifolds of any dimension and codimension into Lie groups equipped with left invariant metrics. As applications, we get a spinorial proof of the Fundamental Theorem for submanifolds into Lie groups, we recover previously known representations of submanifolds in R-n and in the 3-dimensional Lie groups S-3 and E(kappa, tau), and we get a new spinorial representation for surfaces in the 3-dimensional semi-direct products: this achieves the spinorial representations of surfaces in the 3-dimensional homogeneous spaces. We finally indicate how to recover a Weierstrass-type representation for CMC-surfaces in 3-dimensional metric Lie groups recently given by Meeks, Mira, Perez and Ros. (C) 2016 Elsevier B.V. All rights reserved.

【 授权许可】

Free