Almost Hermitian Geometry on Six Dimensional Nilmanifolds

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.