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Forum Mathematicum

Managing Editor: Bruinier, Jan Hendrik

Ed. by Brüdern, Jörg / Cohen, Frederick R. / Droste, Manfred / Duzaar, Frank / Neeb, Karl-Hermann / Noguchi, Junjiro / Shahidi, Freydoon / Sogge, Christopher D. / Wienhard, Anna

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Volume 27, Issue 2 (Mar 2015)

Issues

Balanced Hermitian geometry on 6-dimensional nilmanifolds

Luis Ugarte
  • Departamento de Matemáticas – I.U.M.A., Universidad de Zaragoza, Campus Plaza San Francisco, 50009 Zaragoza, Spain
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/ Raquel Villacampa
  • Centro Universitario de la Defensa – I.U.M.A., Academia General Militar, Crta. de Huesca s/n., 50090 Zaragoza, Spain
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Published Online: 2013-03-14 | DOI: https://doi.org/10.1515/forum-2012-0072

Abstract

The invariant balanced Hermitian geometry of nilmanifolds of dimension 6 is described. We prove that the (restricted) holonomy group of the associated Bismut connection reduces to a proper subgroup of SU(3) if and only if the complex structure is abelian. As an application we show that if J is abelian, then any invariant balanced J-Hermitian structure provides solutions of the Strominger system.

Keywords: Hermitian connection; balanced metric; small deformation; holonomy group; Strominger system

MSC: 53C55; 53C29; 81T30

About the article

Received: 2012-05-21

Revised: 2012-10-13

Published Online: 2013-03-14

Published in Print: 2015-03-01


Funding Source: MICINN (Spain)

Award identifier / Grant number: MTM2008-06540-C02-02

Funding Source: MICINN (Spain)

Award identifier / Grant number: MTM2011-28326-C02-01


Citation Information: Forum Mathematicum, ISSN (Online) 1435-5337, ISSN (Print) 0933-7741, DOI: https://doi.org/10.1515/forum-2012-0072.

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Citing Articles

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[1]
Daniele Angella and Luis Ugarte
Differential Geometry and its Applications, 2017
[2]
Antonio Otal, Luis Ugarte, and Raquel Villacampa
Nuclear Physics B, 2017, Volume 920, Page 442
[3]
A. Latorre, L. Ugarte, and R. Villacampa
Differential Geometry and its Applications, 2017
[4]
M. Ceballos, A. Otal, L. Ugarte, and R. Villacampa
The Journal of Geometric Analysis, 2016, Volume 26, Number 1, Page 252
[5]
ADRIÁN ANDRADA and RAQUEL VILLACAMPA
Transformation Groups, 2016, Volume 21, Number 4, Page 903
[6]
Daniele Angella and Luis Ugarte
Mediterranean Journal of Mathematics, 2016, Volume 13, Number 4, Page 2105
[7]
Marisa Fernández, Stefan Ivanov, Luis Ugarte, and Dimiter Vassilev
Communications in Mathematical Physics, 2015, Volume 339, Number 1, Page 199

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