Sub-semi-Riemannian geometry of general H-type groups

被引：13

作者：

Molina, Mauricio Godoy ^{[1
]}

Korolko, Anna

Markina, Irina ^{[2
]}

机构：

[1] Ecole Polytech, CNRS, CMAP, F-91128 Palaiseau, France

[2] Univ Bergen, Dept Math, N-5020 Bergen, Norway

来源：

BULLETIN DES SCIENCES MATHEMATIQUES | 2013年 / 137卷 / 06期

关键词：

H-type group; Sub-semi-Riemannian geometry; Geodesic; Composition of quadratic forms; Clifford algebra; LORENTZIAN GEOMETRY;

D O I：

10.1016/j.bulsci.2013.05.005

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study a special class of nilpotent Lie groups of step 2, that generalizes the class of the so-called H(eisenberg)-type groups, defined by A. Kaplan in 1980. We change the presence of an inner product to an arbitrary scalar product and relate the construction to the composition of quadratic forms. We present the geodesic equation for sub-semi-Riemannian metric on nilpotent Lie groups of step 2 and solve them for the case of general H-type groups. We also present some results on sectional curvature and the Ricci tensor of semi-Riemannian general H-type groups. (C) 2013 Elsevier Masson SAS. All rights reserved.

引用

页码：805 / 833

页数：29