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

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 $M$ endowed with a symplectic half-flat SU(3)-structure has abelian Lie algebra with dimension bounded by min$\{5,b_1(M)\}$. Moreover, we study the properties of the automorphism group action and we discuss relevant examples. In particular, we provide new complete examples on $T\mathbb{S}^3$ which are invariant under a cohomogeneity one action of SO(4).