Real hypersurfaces in complex hyperbolic two-plane Grassmannians with Reeb invariant Ricci tensor

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• 作者：Gyu Jong Kim ^{hb2107@naver.com" class="auth_mail" title="E-mail the corresponding author} ; Young Jin Suh ; ^{yjsuh@knu.ac.kr" class="auth_mail" title="E-mail the corresponding author}
• 关键词：primary ; 53C40 ; secondary ; 53C15
• 刊名：Differential Geometry and its Applications
• 出版年：2016
• 出版时间：August 2016
• 年：2016
• 卷：47
• 期：Complete
• 页码：14-25
• 全文大小：343 K

文摘

In this paper we first introduce the full expression of the curvature tensor of a real hypersurface M   in complex hyperbolic two-plane Grassmannians SU_2,m/S(U₂⋅U_m)${\mathit{SU}}_{2,m}/S(U_2\cdot U_m)$, m≥2$m\ge 2$ from the equation of Gauss. Next we derive a new formula for the Ricci tensor S of M   in SU_2,m/S(U₂⋅U_m)${\mathit{SU}}_{2,m}/S(U_2\cdot U_m)$. Finally we give a complete classification of Hopf hypersurfaces in complex hyperbolic two-plane Grassmannians SU_2,m/S(U₂⋅U_m)${\mathit{SU}}_{2,m}/S(U_2\cdot U_m)$ with Reeb invariant Ricci tensor, that is, L_ξS=0${\mathcal{L}}_{\xi }S=0$. Each can be described as a tube over a totally geodesic SU_2,m−1/S(U₂⋅U_m−1)${\mathit{SU}}_{2,m-1}/S(U_2\cdot U_{m-1})$ in SU_2,m/S(U₂⋅U_m)${\mathit{SU}}_{2,m}/S(U_2\cdot U_m)$ or a horosphere whose center at infinity is singular.