scholarly journals PARALLEL*-RICCI TENSOR OF REAL HYPERSURFACES IN $\mathbb{C}P^{2}$ AND $\mathbb{C}H^{2}$

2014 ◽  
Vol 18 (6) ◽  
pp. 1991-1998
Author(s):  
George Kaimakamis ◽  
Konstantina Panagiotidou
Keyword(s):  
Ricci Tensor ◽  
Real Hypersurfaces ◽  
Parallel Ricci Tensor

Real Hypersurfaces in ℂP 2 and ℂH 2 with Cyclic Parallel ∗-Ricci Tensor

2021 ◽  
Vol 58 (3) ◽  
pp. 308-318
Author(s):  
Yaning Wang ◽  
Wenjie Wang
Keyword(s):  
Ricci Tensor ◽  
Hyperbolic Plane ◽  
Real Hypersurface ◽  
Three Dimensional ◽  
Real Hypersurfaces ◽  
Complex Projective Plane ◽  
Cyclic Parallel Ricci Tensor ◽  
Complex Projective ◽  
Parallel Ricci Tensor ◽  
Complex Hyperbolic Plane

In this paper, we prove that the ∗-Ricci tensor of a real hypersurface in complex projective plane ℂP 2 or complex hyperbolic plane ℂH 2 is cyclic parallel if and only if the hypersurface is of type (A). We find some three-dimensional real hypersurfaces having non-vanishing and non-parallel ∗-Ricci tensors which are cyclic parallel.

Real hypersurfaces in complex two-plane Grassmannians with parallel Ricci tensor

2012 ◽  
Vol 142 (6) ◽  
pp. 1309-1324 ◽  
Author(s):  
Young Jin Suh
Keyword(s):  
Curvature Tensor ◽  
Ricci Tensor ◽  
Real Hypersurface ◽  
Real Hypersurfaces ◽  
Gauss Equation ◽  
Full Expression ◽  
New Formula ◽  
Parallel Ricci Tensor

We introduce the full expression of the curvature tensor of a real hypersurface M in complex two-plane Grassmannians G2(ℂm+2) from the Gauss equation. We then derive a new formula for the Ricci tensor of M in G2(ℂm+2). Finally, we prove that there does not exist any Hopf real hypersurface in complex two-plane Grassmannians G2(ℂm+2) with parallel Ricci tensor.

A new classification on parallel Ricci tensor for real hypersurfaces in the complex quadric

2020 ◽  
pp. 1-23
Author(s):  
Hyunjin Lee ◽  
Young Jin Suh
Keyword(s):  
Ricci Tensor ◽  
Real Hypersurfaces ◽  
Normal Vector ◽  
Unit Normal Vector ◽  
New Classification ◽  
Normal Vector Field ◽  
Complex Quadric ◽  
Unit Normal Vector Field ◽  
Parallel Ricci Tensor

First we introduce the notion of parallel Ricci tensor ${\nabla }\mathrm {Ric}=0$ for real hypersurfaces in the complex quadric Q m  = SOm+2/SO m SO2 and show that the unit normal vector field N is singular. Next we give a new classification of real hypersurfaces in the complex quadric Q m  = SOm+2/SO m SO2 with parallel Ricci tensor.

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