The *-Ricci Tensor of Real Hypersurfaces in Symmetric Spaces of Rank One or Two
The *-Ricci Tensor of Real Hypersurfaces in Symmetric Spaces of Rank One or Two
复制标题
一阶或二阶对称空间中实超曲面的*-Ricci 张量
DOI：
10.1007/978-4-431-55215-4_18
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发表时间：
2014
期刊：
影响因子：
--
通讯作者：
K. Panagiotidou
中科院分区：
文献类型：
--
作者：
G. Kaimakamis;K. Panagiotidou
复射影和双曲空间，即非平坦复空间形式，是秩为1的对称空间。复二平面格拉斯曼空间是秩为二的对称空间。设M是秩为1或2的对称空间中的真实的超曲面。Berndt，Jeong，Kim，Ortega，Pérez，桑托斯，Suh，Takagi等几何学家从算子和张量场的角度研究了上述空间中的真实的超曲面。本文将分为两个部分。首先，Hamada（真实的hypersurfaces of complex space forms in terms of Ricci *-tensor. Tokyo J.Math.25，473-483（2002））。更确切地说，它将回答是否存在真实的的超曲面，其Ricci张量是平行的，半平行的，即R <$S <$= 0，或伪平行的，即L <$0（Kaimakamis和Panagiotidou，Parallel Ricci tensor of真实的hypersurfaces in and.台湾J. Math.，出现，DOI 10.11650/tjm.18.2014.4271; Kaimakamis和Panagiotidou，真实的超曲面的Ricci张量的平行性条件和。预印本）。其次，给出复二平面Grassmannian中真实的超曲面的Ricci张量的计算公式（Panagiotidou，The Ricci-Ricci tensor of真实的hypersurfaces in complex two-plane Grassmannian，work in progress）。
Complex projective and hyperbolic spaces, i.e. non-flat complex space forms, are symmetric spaces of rank one. Complex two-plane Grassmannians are symmetric spaces of rank two. LetMbe a real hypersurface in a symmetric space of rank one or two. Many geometers, such as Berndt, Jeong, Kim, Ortega, Pérez, Santos, Suh, Takagi and others have studied real hypersurfaces in above spaces in terms of their operators and tensor fields. This paper will be divided into two parts. Firstly, results concerning real hypersurfaces in non-flat complex space forms in terms of their∗-Ricci tensor,S∗, which in case of real hypersurfaces was first studied by Hamada (Real hypersurfaces of complex space forms in terms of Ricci *-tensor. Tokyo J. Math.25, 473–483 (2002)), will be presented. More precisely, it will be answered if there exist or not real hypersurfaces, whose∗-Ricci tensor is parallel, semi-parallel, i.e.R⋅S∗= 0, or pseudo-parallel, i.e.withL≠ 0 (Kaimakamis and Panagiotidou, Parallel∗-Ricci tensor of real hypersurfaces inand. Taiwan. J. Math., to appear, DOI 10.11650/tjm.18.2014.4271; Kaimakamis and Panagiotidou, Conditions of parallelism of∗-Ricci tensor of real hypersurfaces inand. Preprint). Secondly, the formula of∗-Ricci tensor of real hypersurfaces in complex two-plane Grassmannians will be provided (Panagiotidou, The∗-Ricci tensor of real hypersurfaces in complex two-plane Grassmannians, work in progress).