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Real Hypersurfaces in Complex Two-plane Grassmannians with Reeb Parallel Ricci Tensor in the GTW Connection

  • Juan de Dios Pérez (a1), Hyunjin Lee (a2), Young Jin Suh (a3) and Changhwa Woo (a4)

Abstract

There are several kinds of classification problems for real hypersurfaces in complex two-plane Grassmannians ${{G}_{2}}\left( {{\mathbb{C}}^{m+2}} \right)$ . Among them, Suh classified Hopf hypersurfaces in ${{G}_{2}}\left( {{\mathbb{C}}^{m+2}} \right)$ with Reeb parallel Ricci tensor in Levi–Civita connection. In this paper, we introduce the notion of generalized Tanaka–Webster $\left( \text{GTW} \right)$ Reeb parallel Ricci tensor for Hopf hypersurfaces in ${{G}_{2}}\left( {{\mathbb{C}}^{m+2}} \right)$ . Next, we give a complete classification of Hopf hypersurfaces in ${{G}_{2}}\left( {{\mathbb{C}}^{m+2}} \right)$ with $\text{GTW}$ Reeb parallel Ricci tensor.

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