Almost Hermitian Geometry on Six Dimensional Nilmanifolds

Abstract

The fundamental 2-form of an invariant almost Hermitian structure on a 6-dimensional Lie group is described in terms of an action by SO(4)xU(1) on complex projective 3-space. This leads to a combinatorial description of the classes of almost Hermitian structures on the Iwasawa and other nilmanifolds.

22 pages, 2 figures

Cited by in corpus (22)

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• Almost Hermitian 6-Manifolds Revisited
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• Quasi-Kähler manifolds with trivial Chern Holonomy
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• Almost Robinson geometries
• Algebraic dimension and complex subvarieties of hypercomplex nilmanifolds
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• Families of strong KT structures in six dimensions
• Special metrics in $G_2$ geometry
• The space of leftinvariant orthogonal almost complex structures on 6-dimensional Lie groups
• A note on Canonical Ricci forms on 2-step nilmanifolds