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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

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1435-5337
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Volume 31, Issue 1

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

Fabio Podestà
/ Alberto Raffero
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 $\mathrm{SU}\left(3\right)$-structure has Abelian Lie algebra with dimension bounded by $\mathrm{min}\left\{5,{b}_{1}\left(M\right)\right\}$. Moreover, we study the properties of the automorphism group action and we discuss relevant examples. In particular, we provide new complete examples on $T{𝕊}^{3}$ which are invariant under a cohomogeneity one action of $\mathrm{SO}\left(4\right)$.

MSC 2010: 53C10; 57S15

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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,

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