Almost Hermitian Structures with Parallel Torsion

Abstract

The characteristic connection of an almost hermitian structure is a hermitian connection with totally skew-symmetric torsion. The case of parallel torsion in dimension six is of particular interest. In this work, we give a full classification of the algebraic types of the torsion form, and, based on this, undertake a systematic investigation into the possible geometries. Numerous naturally reductive spaces are constructed and classified as well as examples on nilmanifolds given.

36 pages

References in corpus (2)

• SU(3)-instantons and $G_2,Spin(7)$-heterotic string solitons
• Almost Hermitian 6-Manifolds Revisited

Cited by in corpus (14)

• The Srni lectures on non-integrable geometries with torsion
• Metric connections with parallel skew-symmetric torsion
• Compact supersymmetric solutions of the heterotic equations of motion in dimension 5
• Spin(7)-manifolds with parallel torsion form
• The classification of naturally reductive homogeneous spaces in dimensions $n\le 6$
• The Killing spinor equation with higher order potentials
• A new $\frac{1}{2}$-Ricci type formula on the spinor bundle and applications
• The Mean Curvature of Special Lagrangian 3-folds in SU(3)-Structures with Torsion
• A note on generalized Dirac eigenvalues for split holonomy and torsion
• Twistorial eigenvalue estimates for generalized Dirac operators with torsion
• On the metric structure of some non-Kähler complex threefolds
• Einstein manifolds with skew torsion
• Harmonic $SU(3)$- and $G_2$-structures via spinors
• Homogeneous almost complex structures in dimension 6 with semi-simple isotropy