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 T3 which are invariant under a cohomogeneity one action of SO(4).
On the automorphism group of a symplectic half-flat 6-manifold
Raffero, Alberto
2019-01-01
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 T3 which are invariant under a cohomogeneity one action of SO(4).
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