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

Mauricio Godoy Molina; Anna Korolko; Irina Markina

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

Differential Geometry 2015-08-13 v1

Authors: Mauricio Godoy Molina , Anna Korolko , Irina Markina

Abstract

We introduce a special class of nilpotent Lie groups of step 2, that generalizes the so called $H$ (eisenberg)-type groups, defined by A. Kaplan in 1980. We change the presence of 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 general $H$ -type groups.

Keywords

sub-semi-Riemannian geometry $H$-type groups nilpotent Lie groups geodesic equation sectional curvature Ricci tensor

Cite

@article{arxiv.1207.5608,
  title  = {Sub-semi-Riemannian geometry of general $H$-type groups},
  author = {Mauricio Godoy Molina and Anna Korolko and Irina Markina},
  journal= {arXiv preprint arXiv:1207.5608},
  year   = {2015}
}

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27 pages, no figures

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

Abstract

Keywords

Cite

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