The axiom of {\theta}-holomorphic 2-planes in the almost Hermitian geometry

TL;DR

This paper introduces the axiom of { heta}-holomorphic 2-planes in almost Hermitian geometry and proves that satisfying this axiom implies the manifold is a real space form, revealing a geometric characterization.

Contribution

It introduces the { heta}-holomorphic 2-plane axiom and establishes its equivalence to the manifold being a real space form in almost Hermitian geometry.

Findings

Satisfaction of the { heta}-holomorphic 2-plane axiom characterizes real space forms.

The axiom applies for fixed { heta} in (0, { heta}), linking geometric conditions to curvature.

Provides a new geometric criterion for classifying almost Hermitian manifolds.

Abstract

The axiom of {\theta}-holomorphic 2-planes is introduced. It is proved, that if an almost Hermitian manifold satisfies this axiom for a fixed {\theta}, 0< {\theta}< {\pi}/2, then it is a real space form.