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Advances in Geometry

Managing Editor: Grundhöfer, Theo / Joswig, Michael

Editorial Board: Bamberg, John / Bannai, Eiichi / Cavalieri, Renzo / Coskun, Izzet / Duzaar, Frank / Eberlein, Patrick / Gentili, Graziano / Henk, Martin / Kantor, William M. / Korchmaros, Gabor / Kreuzer, Alexander / Lagarias, Jeffrey C. / Leistner, Thomas / Löwen, Rainer / Ono, Kaoru / Ratcliffe, John G. / Scheiderer, Claus / Van Maldeghem, Hendrik / Weintraub, Steven H. / Weiss, Richard


IMPACT FACTOR 2018: 0.789

CiteScore 2018: 0.73

SCImago Journal Rank (SJR) 2018: 0.329
Source Normalized Impact per Paper (SNIP) 2018: 0.908

Mathematical Citation Quotient (MCQ) 2018: 0.53

Online
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1615-7168
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Volume 15, Issue 4

Issues

On the geometrical properties of solvable Lie groups

Mansour Aghasi
  • Corresponding author
  • Department of Mathematical Sciences, Isfahan University of Technology, Isfahan, 84156-83111, Iran
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/ Mehri Nasehi
Published Online: 2015-10-06 | DOI: https://doi.org/10.1515/advgeom-2015-0025

Abstract

In [3] Bozek introduced a class of solvable Lie groups M2n+1. Calvaruso, Kowalski and Marinosci in [9] have studied homogeneous geodesics on these homogeneous spaces with an arbitrary odd dimension. In [1] we have studied some other geometrical properties on these spaces with dimension five. Our aim in this paper is to extend those geometrical properties for an arbitrary odd dimension in both Riemannian and Lorentzian cases. In fact we first obtain all of the descriptions of their homogeneous Lorentzian and Riemannian structures and their types. Then we calculate the energy of an arbitrary left-invariant vector field X on these spaces and in the Lorentzian case we prove that no left-invariant unit time-like vector fields on these spaces are critical points for the space-like energy. There is also a proof of non-existence of invariant contact structures and left-invariant Ricci solitons on these homogeneous spaces.

Keywords: Homogeneous structures; left-invariant Ricci solitons; harmonicity of invariant vector fields; invariant contact structures; solvable Lie groups

About the article

Received: 2013-12-07

Revised: 2014-05-14

Published Online: 2015-10-06

Published in Print: 2015-10-01


Citation Information: Advances in Geometry, Volume 15, Issue 4, Pages 507–517, ISSN (Online) 1615-7168, ISSN (Print) 1615-715X, DOI: https://doi.org/10.1515/advgeom-2015-0025.

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Citing Articles

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[1]
Mehri Nasehi
Archivum Mathematicum, 2016, Number 4, Page 221
[2]
Mehri Nasehi
Mediterranean Journal of Mathematics, 2019, Volume 16, Number 2
[3]
Mehri Nasehi
Czechoslovak Mathematical Journal, 2016, Volume 66, Number 2, Page 547

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