Almost Hermitian Geometry on Six Dimensional Nilmanifolds
E. Abbena, S. Garbiero, S. Salamon

TL;DR
This paper characterizes invariant almost Hermitian structures on 6-dimensional nilmanifolds using group actions, providing a combinatorial classification for specific examples like the Iwasawa manifold.
Contribution
It introduces a novel combinatorial approach to classify almost Hermitian structures on 6D nilmanifolds via SO(4)×U(1) actions.
Findings
Describes the fundamental 2-form in terms of SO(4)×U(1) action.
Provides a classification scheme for structures on Iwasawa and similar nilmanifolds.
Establishes a link between geometric structures and combinatorial data.
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.
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Taxonomy
TopicsGeometry and complex manifolds · Geometric Analysis and Curvature Flows · Geometric and Algebraic Topology
