Decomposition of Euclidean Nearly K\"ahler submanifolds

TL;DR

This paper investigates the structure of nearly K"ahler submanifolds in Euclidean space, revealing conditions under which they decompose into products of simpler nearly K"ahler manifolds, enhancing understanding of their geometric properties.

Contribution

It introduces a decomposition theorem for nearly K"ahler submanifolds based on foliation and umbilic distributions, providing new insights into their geometric structure.

Findings

Decomposition of nearly K"ahler submanifolds into product manifolds

Identification of conditions for the leaf space to be nearly K"ahler

Characterization of the submanifold structure in Euclidean space

Abstract

We study the foliation space of complex and invariant (by torsion of intrinsic Hermitian connection) umbilic distribution on an isometric immersion from a nearly K\"ahler manifold $M$ into the Euclidean space. Under suitable conditions this leaf space is nearly K\"ahler and $M$ can be decomposed into a product of this leaf space and a 6-dimensional locally homogeneous nearly K\"ahler manifold.