Real Hypersurfaces in complex two-plane Grassmannians with recurrent Ricci tensor

TL;DR

This paper introduces a new concept of a generalized Reeb recurrent Ricci tensor in complex two-plane Grassmannians and proves that such hypersurfaces cannot exist under these conditions.

Contribution

It defines a novel generalized Reeb recurrent Ricci tensor in complex Grassmannians and establishes a non-existence result for hypersurfaces with this property.

Findings

Non-existence of hypersurfaces with generalized Reeb recurrent Ricci tensor

Introduction of a new notion of Ricci tensor in complex Grassmannians

Theoretical proof of non-existence under specified conditions

Abstract

In this paper, we have introduced a new notion of generalized Tanaka-Webster Reeb recurrent Ricci tensor in complex two-plane Grassmannians $G_2({\mathbb C}^{m+2})$. Next, we give a non-existence property for real hypersurfaces $M$ in $G_2({\mathbb C}^{m+2})$ with such a condition.