The axiom of coholomorphic (2n+1)-spheres in the almost Hermitian geometry

TL;DR

This paper proves that an almost Hermitian manifold satisfying the axiom of coholomorphic spheres must be conformally flat, revealing a significant geometric property linked to this axiom.

Contribution

It establishes a new characterization of conformal flatness in almost Hermitian manifolds based on the axiom of coholomorphic spheres.

Findings

Almost Hermitian manifolds satisfying the axiom are conformally flat.

The axiom imposes strong geometric constraints on the manifold.

Provides a new criterion for conformal flatness in complex geometry.

Abstract

It is proved, that if an almost Hermitian manifold satisfies the axiom of coholomorphic spheres, it is conformal flat.