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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. / Scharlau, Rudolf / Scheiderer, Claus / Van Maldeghem, Hendrik / Weintraub, Steven H. / Weiss, Richard

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Volume 18, Issue 3

Issues

Harmonicity of vector fields on a class of Lorentzian solvable Lie groups

Ju Tan
  • School of Mathematics and Physics Science and Engineering, Anhui University of Technology, Ma’anshan, 243032, People’s Republic of China
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/ Shaoqiang Deng
  • Corresponding author
  • School of Mathematical Sciences and LPMC, Nankai University, Tianjin 300071, People’s Republic of China
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Published Online: 2018-07-18 | DOI: https://doi.org/10.1515/advgeom-2017-0014

Abstract

In this paper, we consider a special class of solvable Lie groups such that for any x, y in their Lie algebras, [x, y] is a linear combination of x and y. We investigate the harmonicity properties of invariant vector fields of this kind of Lorentzian Lie groups. It is shown that any invariant unit time-like vector field is spatially harmonic. Moreover, we determine all vector fields which are critical points of the energy functional restricted to the space of smooth vector fields.

Keywords: Harmonic sections; harmonic maps; Lie group; spatially harmonic

MSC 2010: 53C50; 53C43

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About the article


Received: 2015-08-19

Revised: 2016-06-06

Published Online: 2018-07-18

Published in Print: 2018-07-26


Funding: This work was supported by NSFC (no. 11271198, 51535008, 11671212) and SRFDP of China.


Citation Information: Advances in Geometry, Volume 18, Issue 3, Pages 337–344, ISSN (Online) 1615-7168, ISSN (Print) 1615-715X, DOI: https://doi.org/10.1515/advgeom-2017-0014.

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