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Forum Mathematicum

Managing Editor: Bruinier, Jan Hendrik

Ed. by Cohen, Frederick R. / Droste, Manfred / Darmon, Henri / Duzaar, Frank / Echterhoff, Siegfried / Gordina, Maria / Neeb, Karl-Hermann / Shahidi, Freydoon / Sogge, Christopher D. / Takayama, Shigeharu / Wienhard, Anna


IMPACT FACTOR 2018: 0.867

CiteScore 2018: 0.71

SCImago Journal Rank (SJR) 2018: 0.898
Source Normalized Impact per Paper (SNIP) 2018: 0.964

Mathematical Citation Quotient (MCQ) 2018: 0.71

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1435-5337
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Volume 26, Issue 2

Issues

On seven-dimensional quaternionic contact solvable Lie groups

Diego Conti / Marisa Fernández
  • Departamento de Matemáticas, Facultad de Ciencia y Tecnología, Universidad del País Vasco, Apartado 644, 48080 Bilbao, Spain
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/ José A. Santisteban
  • Departamento de Matemáticas, Facultad de Ciencia y Tecnología, Universidad del País Vasco, Apartado 644, 48080 Bilbao, Spain
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Published Online: 2012-01-25 | DOI: https://doi.org/10.1515/forum-2011-0128

Abstract

We answer in the affirmative a question posed by Ivanov and Vassilev on the existence of a seven-dimensional quaternionic contact manifold with closed fundamental 4-form and non-vanishing torsion endomorphism. Moreover, we show an approach to the classification of seven-dimensional solvable Lie groups having an integrable left invariant quaternionic contact structure. In particular, we prove that the unique seven-dimensional nilpotent Lie group admitting such a structure is the quaternionic Heisenberg group.

Keywords: Quaternionic-contact structures; Biquard connection; torsion endomorphism

MSC: 53C26; 53C25

About the article

Received: 2011-11-08

Published Online: 2012-01-25

Published in Print: 2014-03-01


Funding Source: MICINN (Spain)

Award identifier / Grant number: MTM2008-06540-C02-01

Funding Source: UFI (UPV/EHU)

Award identifier / Grant number: 11/52


Citation Information: Forum Mathematicum, Volume 26, Issue 2, Pages 547–576, ISSN (Online) 1435-5337, ISSN (Print) 0933-7741, DOI: https://doi.org/10.1515/forum-2011-0128.

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