scholarly journals A complete classification of real hypersurfaces in $\mathbb{C}P^{2}$ and $\mathbb{C}H^{2}$ with generalized $\xi-$parallel Jacobi structure Operator

2016 ◽  
Vol 23 (1) ◽  
pp. 103-113
Author(s):  
Th. Theofanidis
Keyword(s):  
Complete Classification ◽  
Real Hypersurfaces ◽  
Jacobi Structure

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 Real Hypersurfaces of Nonflat Complex Projective Planes Whose Jacobi Structure Operator Satisfies a Generalized Commutative Condition

2016 ◽  
Vol 2016 ◽  
pp. 1-6
Author(s):  
Theocharis Theofanidis
Keyword(s):  
Projective Plane ◽  
Projective Planes ◽  
Additional Restriction ◽  
Real Hypersurfaces ◽  
Specific Function ◽  
Complex Projective Plane ◽  
Jacobi Structure ◽  
Complex Projective

Real hypersurfaces satisfying the conditionϕl=lϕ(l=R(·,ξ)ξ)have been studied by many authors under at least one more condition, since the class of these hypersurfaces is quite tough to be classified. The aim of the present paper is the classification of real hypersurfaces in complex projective planeCP2satisfying a generalization ofϕl=lϕunder an additional restriction on a specific function.

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.

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].

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).

REAL HYPERSURFACES OF NON-FLAT COMPLEX SPACE FORMS WITH GENERALIZED ξ-PARALLEL JACOBI STRUCTURE OPERATOR

2015 ◽  
Vol 58 (3) ◽  
pp. 677-687
Author(s):  
TH. THEOFANIDIS
Keyword(s):  
Tangent Space ◽  
Complex Space ◽  
Real Hypersurfaces ◽  
Space Forms ◽  
Jacobi Structure ◽  
Complex Space Forms ◽  
First Time

AbstractThe aim of the present paper is the classification of real hypersurfaces M equipped with the condition Al = lA, l = R(., ξ)ξ, restricted in a subspace of the tangent space TpM of M at a point p. This class is large and difficult to classify, therefore a second condition is imposed: (∇ξl)X = ω(X)ξ + ψ(X)lX, where ω(X), ψ(X) are 1-forms. The last condition is studied for the first time and is much weaker than ∇ξl = 0 which has been studied so far. The Jacobi Structure Operator satisfying this weaker condition can be called generalized ξ-parallel Jacobi Structure Operator.

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.

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

2016 ◽  
Vol 59 (4) ◽  
pp. 721-733
Author(s):  
Juan de Dios Pérez ◽  
Hyunjin Lee ◽  
Young Jin Suh ◽  
Changhwa Woo
Keyword(s):  
Ricci Tensor ◽  
Complete Classification ◽  
Real Hypersurfaces ◽  
Classification Problems ◽  
Hopf Hypersurfaces ◽  
Civita Connection ◽  
Levi Civita Connection ◽  
Parallel Ricci Tensor

AbstractThere are several kinds of classification problems for real hypersurfaces in complex two-plane Grassmannians G2(ℂm+2). Among them, Suh classified Hopf hypersurfaces in G2(ℂm+2) with Reeb parallel Ricci tensor in Levi–Civita connection. In this paper, we introduce the notion of generalized Tanaka–Webster (GTW) Reeb parallel Ricci tensor for Hopf hypersurfaces in G2(ℂm+2). Next, we give a complete classification of Hopf hypersurfaces in G2(ℂm+2) with GTW Reeb parallel Ricci tensor.

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.

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