A Study of Submanifolds of the Complex Grassmannian Manifold with Parallel Second Fundamental Form

TL;DR

This paper extends a theorem characterizing certain compact Kaehler submanifolds by holomorphic pinching to submanifolds of complex Grassmannian manifolds, advancing understanding of their geometric properties.

Contribution

It generalizes Ros's theorem from Kaehler submanifolds to submanifolds of complex Grassmannians with parallel second fundamental form.

Findings

Extended characterization of submanifolds in complex Grassmannians.

Identified conditions for holomorphic pinching in new settings.

Provided geometric criteria for submanifold classification.

Abstract

We prove an extension of a theorem of A.Ros on a characterization of seven compact Kaehler submanifolds by holomorphic pinching to certain submanifolds of the complex Grassmannian manifolds.