On the automorphism group of a symplectic half-flat 6-manifold
Fabio Podest\`a, Alberto Raffero

TL;DR
This paper investigates the automorphism group of compact 6-manifolds with symplectic half-flat SU(3)-structures, establishing bounds on its dimension and exploring its properties through examples, including new invariant structures on tangent bundles of spheres.
Contribution
It proves that the automorphism group's Lie algebra is abelian with bounded dimension and provides new explicit examples with symmetry properties.
Findings
Automorphism Lie algebra is abelian with dimension ≤ min{5, b_1(M)}.
Automorphism group action properties are characterized.
New examples on T S^3 with cohomogeneity one SO(4) action are constructed.
Abstract
We prove that the automorphism group of a compact 6-manifold endowed with a symplectic half-flat SU(3)-structure has abelian Lie algebra with dimension bounded by min. Moreover, we study the properties of the automorphism group action and we discuss relevant examples. In particular, we provide new complete examples on which are invariant under a cohomogeneity one action of SO(4).
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