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

Pérez, Juan de Dios ; Lee, Hyunjin ; Suh, Young Jin ; Woo, Changhwa

Canadian mathematical bulletin, Tome 59 (2016) no. 4, pp. 721-733

Résumé

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.

Détail

DOI : 10.4153/CMB-2016-035-x

Mots-clés : 53C40, 53C15, complex two-plane Grassmannian, real hypersurface, Hopf hypersurface, generalized Tanaka-Webster connection, parallelism, Reeb parallelism, Ricci tensor

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