Generalized Tanaka-Webster Parallel Ricci tensor in complex two-plane Grassmannians

TL;DR

This paper proves that Hopf real hypersurfaces in complex two-plane Grassmannians cannot have a Ricci tensor that is parallel with respect to the generalized Tanaka-Webster connection, establishing a non-existence result.

Contribution

It introduces a non-existence theorem for Hopf real hypersurfaces with parallel Ricci tensor in this geometric setting.

Findings

No Hopf real hypersurfaces with parallel Ricci tensor exist in complex two-plane Grassmannians.

The result extends understanding of curvature properties in complex Grassmannian geometry.

The proof relies on properties of the generalized Tanaka-Webster connection.

Abstract

We prove the non-existence of Hopf real hypersurfaces in complex two-plane Grassmannians whose Ricci tensor is parallel with respect to the generalized Tanaka-Webster connection.