Yamabe and gradient Yamabe solitons on real hypersurfaces in the complex quadric

2021 ◽  
Author(s):  
Sudhakar K. Chaubey ◽  
Hyunjin Lee ◽  
Young Jin Suh
Keyword(s):  
Complete Classification ◽  
Real Hypersurfaces ◽  
Complex Quadric ◽  
Yamabe Solitons

In this paper, we give a complete classification of Yamabe solitons and gradient Yamabe solitons on real hypersurfaces in the complex quadric [Formula: see text]. In the following, as an application, we show a complete classification of quasi-Yamabe and gradient quasi-Yamabe solitons on Hopf real hypersurfaces in the complex quadric [Formula: see text].

Real hypersurfaces in the complex quadric with Reeb parallel shape operator

2014 ◽  
Vol 25 (06) ◽  
pp. 1450059 ◽  
Author(s):  
Young Jin Suh
Keyword(s):  
Shape Operator ◽  
Complete Classification ◽  
Real Hypersurfaces ◽  
Complete Proof ◽  
Complex Quadric ◽  
Parallel Shape Operator ◽  
Codazzi Type ◽  
Reeb Parallel Shape Operator

First, we introduce the notion of shape operator of Codazzi type for real hypersurfaces in the complex quadric Qm = SOm+2/SOmSO2. Next, we give a complete proof of non-existence of real hypersurfaces in Qm = SOm+2/SOmSO2 with shape operator of Codazzi type. Motivated by this result we have given a complete classification of real hypersurfaces in Qm = SOm+2/SOmSO2 with Reeb parallel shape operator.

Real Hypersurfaces in the Complex Quadric with Lie Invariant Structure Jacobi Operator

2019 ◽  
Vol 63 (1) ◽  
pp. 204-221
Author(s):  
Young Jin Suh ◽  
Gyu Jong Kim
Keyword(s):  
Jacobi Operator ◽  
Complete Classification ◽  
Real Hypersurfaces ◽  
Normal Vector ◽  
Invariant Structure ◽  
Normal Vector Field ◽  
Jacobi Operators ◽  
Complex Quadric ◽  
Unit Normal Vector Field

AbstractWe introduce the notion of Lie invariant structure Jacobi operators for real hypersurfaces in the complex quadric $Q^{m}=SO_{m+2}/SO_{m}SO_{2}$. The existence of invariant structure Jacobi operators implies that the unit normal vector field $N$ becomes $\mathfrak{A}$-principal or $\mathfrak{A}$-isotropic. Then, according to each case, we give a complete classification of real hypersurfaces in $Q^{m}=SO_{m+2}/SO_{m}SO_{2}$ with Lie invariant structure Jacobi operators.

Real hypersurfaces in the complex quadric with Killing normal Jacobi operator

2018 ◽  
Vol 149 (2) ◽  
pp. 279-296 ◽  
Author(s):  
Young Jin Suh
Keyword(s):  
Jacobi Operator ◽  
Complete Classification ◽  
Real Hypersurfaces ◽  
Normal Vector ◽  
Unit Normal Vector ◽  
Normal Vector Field ◽  
Complex Quadric ◽  
Unit Normal Vector Field ◽  
Normal Jacobi Operator

AbstractWe introduce the notion of Killing normal Jacobi operator for real hypersurfaces in the complex quadricQm=SOm+2/SOmSO2. The Killing normal Jacobi operator implies that the unit normal vector fieldNbecomes 𝔄-principal or 𝔄-isotropic. Then according to each case, we give a complete classification of real hypersurfaces inQm=SOm+2/SOmSO2with Killing normal Jacobi operator.

scholarly journals On real hypersurfaces in quaternionic projective space with𝒟⊥-recurrent second fundamental tensor

1999 ◽  
Vol 22 (1) ◽  
pp. 109-117
Author(s):  
Young Jin Suh ◽  
Juan De Dios Pérez
Keyword(s):  
Projective Space ◽  
Complete Classification ◽  
Real Hypersurfaces ◽  
Quaternionic Projective Space ◽  
Fundamental Tensor ◽  
Orthogonal Distribution

In this paper, we give a complete classification of real hypersurfaces in a quaternionic projective spaceQPmwith𝒟⊥-recurrent second fundamental tensor under certain condition on the orthogonal distribution𝒟.

scholarly journals Pseudo-Einstein real hypersurfaces in complex two-plane Grassmannians

2006 ◽  
Vol 73 (2) ◽  
pp. 183-200 ◽  
Author(s):  
Young Jin Suh
Keyword(s):  
Complete Classification ◽  
Real Hypersurfaces

In this paper we give a complete classification of -invariant or Hopf pseudo-Einstein real hypersurfaces in complex two-plane Grassmannians G2(ℂm+2).

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.

A classification of Ricci semi-symmetric real hypersurfaces in the complex quadric

2021 ◽  
Vol 164 ◽  
pp. 104177
Author(s):  
Hyunjin Lee ◽  
Young Jin Suh ◽  
Changhwa Woo
Keyword(s):  
Real Hypersurfaces ◽  
Complex Quadric

A certain η-parallelism on real hypersurfaces in a nonflat complex space form

2021 ◽  
Vol 71 (6) ◽  
pp. 1553-1564
Author(s):  
Kazuhiro Okumura
Keyword(s):  
Tensor Field ◽  
Complex Space ◽  
Space Form ◽  
Complete Classification ◽  
Complex Space Form ◽  
Real Hypersurfaces ◽  
Killing Tensor ◽  
Hopf Hypersurfaces

Abstract In this paper, we give the complete classification of real hypersurfaces in a nonflat complex space form from the viewpoint of the η-parallelism of the tensor field h(= (1/2)𝓛 ξ ϕ). In addition we investigate real hypersurfaces whose tensor h is either Killing type or transversally Killing tensor. In particular, we shall determine Hopf hypersurfaces whose tensor h is transversally Killing tensor by using an application of the classification of real hypersurfaces admitting η-parallelism with respect to the tensor h.

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