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Forum Mathematicum

Managing Editor: Bruinier, Jan Hendrik

Ed. by Blomer, Valentin / Cohen, Frederick R. / Droste, Manfred / Duzaar, Frank / Echterhoff, Siegfried / Frahm, Jan / Gordina, Maria / Shahidi, Freydoon / Sogge, Christopher D. / Takayama, Shigeharu / Wienhard, Anna


IMPACT FACTOR 2018: 0.867

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1435-5337
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Volume 31, Issue 1

Issues

On the automorphism group of a symplectic half-flat 6-manifold

Fabio PodestàORCID iD: https://orcid.org/0000-0002-3132-0483 / Alberto RafferoORCID iD: https://orcid.org/0000-0003-1413-0327
Published Online: 2018-09-20 | DOI: https://doi.org/10.1515/forum-2018-0137

Abstract

We prove that the automorphism group of a compact 6-manifold M endowed with a symplectic half-flat SU(3)-structure has Abelian Lie algebra with dimension bounded by min{5,b1(M)}. Moreover, we study the properties of the automorphism group action and we discuss relevant examples. In particular, we provide new complete examples on T𝕊3 which are invariant under a cohomogeneity one action of SO(4).

Keywords: SU(3)-structure; automorphism group; cohomogeneity one action

MSC 2010: 53C10; 57S15

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About the article


Received: 2018-06-06

Published Online: 2018-09-20

Published in Print: 2019-01-01


The authors were supported by GNSAGA of INdAM – Istituto Nazionale di Alta Matematica.


Citation Information: Forum Mathematicum, Volume 31, Issue 1, Pages 265–273, ISSN (Online) 1435-5337, ISSN (Print) 0933-7741, DOI: https://doi.org/10.1515/forum-2018-0137.

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