Normal split submanifolds of rational homogeneous spaces

TL;DR

This paper proves that submanifolds with a splitting normal sequence in rational homogeneous spaces are themselves rational homogeneous, revealing a structural inheritance property.

Contribution

It establishes that normal split submanifolds of rational homogeneous spaces are necessarily rational homogeneous, a new structural insight.

Findings

Normal split submanifolds are rational homogeneous

The normal sequence splitting implies the submanifold inherits homogeneity

Structural inheritance in rational homogeneous spaces

Abstract

Let $M \subset X$ be a submanifold of a rational homogeneous space $X$ such that the normal sequence splits. We prove that $M$ is also rational homogeneous.