Twisting Hermitian and hypercomplex geometries

Abstract

A twist construction for manifolds with torus action is described generalising certain T-duality examples and constructions in hypercomplex geometry. It is applied to complex, SKT, hypercomplex and HKT manifolds to construct compact simply-connected examples. In particular, we find hypercomplex manifolds that admit no compatible HKT metric, and HKT manifolds whose Obata connection has holonomy contained in $SL(n,\mathbb{H})$.

27 pages

Cited by in corpus (11)

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• Twist geometry of the c-map
• Existence of HKT metrics on hypercomplex manifolds of real dimension 8
• Weighted K-stability and coercivity with applications to extremal Kahler and Sasaki metrics
• Symmetries of quaternionic Kähler manifolds with $S^1$-symmetry
• Curvature of quaternionic Kähler manifolds with $S^1$-symmetry
• Solvable groups and a shear construction
• The c-map as a functor on certain variations of Hodge structure
• Quaternionic Bott-Chern cohomology and existence of HKT metrics
• A class of locally inhomogeneous complete quaternionic Kähler manifolds
• Symmetries of one-loop deformed q-map spaces