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

[摘要] There are several kinds of classification problems for real hypersurfaces in complex two-plane Grassmannians $G_2({mathbb C}^{m+2})$. Among them, Suh classified Hopf hypersurfaces $M$ in $G_2({mathbb C}^{m+2})$ with Reeb parallel Ricci tensor in Levi-Civita connection. In this paper, we introduce the notion of generalized Tanaka-Webster (in shortly, GTW) Reeb parallel Ricci tensor for Hopf hypersurface $M$ in $G_2({mathbb C}^{m+2})$. Next, we give a complete classification of Hopf hypersurfaces in $G_2({mathbb C}^{m+2})$ with GTW Reebparallel Ricci tensor.

[学科分类] 数学（综合）

[关键词] Complex two-plane Grassmannian;real hypersurface;Hopf hypersurface;generalized Tanaka-Webster connection;parallelism;Reeb parallelism;Ricci tensor