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

Canadian mathematical bulletin

Juan de Dios Pérez¹  Young Jin Suh²  Hyunjin Lee⁴  Changhwa Woo³ 

[1] Departamento de Geometria y Topologia, Universidad de Granada, 18071-Granada, Spain;Department of Mathematics and Research Institute of Real and Complex Manifolds, Kyungpook National University, Daegu 702-701, Republic of Korea;Department of Mathematics, Kyungpook National University , Daegu 702-701, Republic of Korea;Research Institute of Real and Complex Manifolds, Kyungpook National University, Daegu 702-701, Republic of Korea

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

DOI  :  10.4153/CMB-2016-035-x

学科分类：数学（综合）

来源: University of Toronto Press * Journals Division

【 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.

【 授权许可】

Unknown