On the geometry of some para-hypercomplex Lie groups

H. R. Salimi Moghaddam

Archivum Mathematicum (2009)

  • Volume: 045, Issue: 3, page 159-170
  • ISSN: 0044-8753

Abstract

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In this paper, firstly we study some left invariant Riemannian metrics on para-hypercomplex 4-dimensional Lie groups. In each Lie group, the Levi-Civita connection and sectional curvature have been given explicitly. We also show these spaces have constant negative scalar curvatures. Then by using left invariant Riemannian metrics introduced in the first part, we construct some left invariant Randers metrics of Berwald type. The explicit formulas for computing flag curvature have been obtained in all cases. Some of these Finsler Lie groups are of non-positive flag curvature.

How to cite

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Salimi Moghaddam, H. R.. "On the geometry of some para-hypercomplex Lie groups." Archivum Mathematicum 045.3 (2009): 159-170. <http://eudml.org/doc/250690>.

@article{SalimiMoghaddam2009,
abstract = {In this paper, firstly we study some left invariant Riemannian metrics on para-hypercomplex 4-dimensional Lie groups. In each Lie group, the Levi-Civita connection and sectional curvature have been given explicitly. We also show these spaces have constant negative scalar curvatures. Then by using left invariant Riemannian metrics introduced in the first part, we construct some left invariant Randers metrics of Berwald type. The explicit formulas for computing flag curvature have been obtained in all cases. Some of these Finsler Lie groups are of non-positive flag curvature.},
author = {Salimi Moghaddam, H. R.},
journal = {Archivum Mathematicum},
keywords = {para-hypercomplex structure; left invariant Riemannian metric; Randers metric; Berwald metric; sectional curvature; flag curvature; para-hypercomplex structure; left invariant Riemannian metric; Randers metric; Berwald metric; sectional curvature; flag curvature},
language = {eng},
number = {3},
pages = {159-170},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {On the geometry of some para-hypercomplex Lie groups},
url = {http://eudml.org/doc/250690},
volume = {045},
year = {2009},
}

TY - JOUR
AU - Salimi Moghaddam, H. R.
TI - On the geometry of some para-hypercomplex Lie groups
JO - Archivum Mathematicum
PY - 2009
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 045
IS - 3
SP - 159
EP - 170
AB - In this paper, firstly we study some left invariant Riemannian metrics on para-hypercomplex 4-dimensional Lie groups. In each Lie group, the Levi-Civita connection and sectional curvature have been given explicitly. We also show these spaces have constant negative scalar curvatures. Then by using left invariant Riemannian metrics introduced in the first part, we construct some left invariant Randers metrics of Berwald type. The explicit formulas for computing flag curvature have been obtained in all cases. Some of these Finsler Lie groups are of non-positive flag curvature.
LA - eng
KW - para-hypercomplex structure; left invariant Riemannian metric; Randers metric; Berwald metric; sectional curvature; flag curvature; para-hypercomplex structure; left invariant Riemannian metric; Randers metric; Berwald metric; sectional curvature; flag curvature
UR - http://eudml.org/doc/250690
ER -

References

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