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.

𝔻-recurrent ∗-Ricci tensor on three-dimensional real hypersurfaces in nonflat complex space forms

2020 ◽  
Vol 70 (4) ◽  
pp. 903-908
Author(s):  
Yaning Wang
Keyword(s):  
Ricci Tensor ◽  
Real Hypersurface ◽  
Complex Space ◽  
Short Note ◽  
Three Dimensional ◽  
Affirmative Answer ◽  
Real Hypersurfaces ◽  
Space Forms ◽  
Nonflat Complex Space Forms ◽  
Complex Space Forms

AbstractKaimakamis and Panagiotidou in [Taiwanese J. Math. 18(6) (2014), 1991–1998] proposed an open question: are there real hypersurfaces in nonflat complex space forms whose ∗-Ricci tensor satisfies the condition of 𝔻-parallelism? In this short note, we present an affirmative answer and prove that a three-dimensional real hypersurface in a nonflat complex space form has 𝔻-parallel ∗-Ricci tensor if and only if it is locally congruent to either a geodesic hypersphere of radius r in ℂ H2(c) with $\begin{array}{} \displaystyle \tanh(\frac{\sqrt{|c|}}{2}r) = \frac{1}{2} \end{array}$ or a ruled real hypersurface.

scholarly journals Lie Derivatives and Ricci Tensor on Real Hypersurfaces in Complex Two-plane Grassmannians

2018 ◽  
Vol 61 (3) ◽  
pp. 543-552
Author(s):  
Imsoon Jeong ◽  
Juan de Dios Pérez ◽  
Young Jin Suh ◽  
Changhwa Woo
Keyword(s):  
Vector Field ◽  
Differential Operator ◽  
Ricci Tensor ◽  
Real Hypersurface ◽  
Real Hypersurfaces ◽  
Reeb Vector ◽  
Reeb Vector Field ◽  
Lie Derivatives ◽  
Lie Derivation

AbstractOn a real hypersurface M in a complex two-plane Grassmannian G2() we have the Lie derivation and a differential operator of order one associated with the generalized Tanaka–Webster connection . We give a classification of real hypersurfaces M on G2() satisfying , where ξ is the Reeb vector field on M and S the Ricci tensor of M.

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.

scholarly journals On inextensible flows of tangent developable of biharmonic B-Slant helices according to Bishop frames in the special 3-dimensional Kenmotsu manifold

2011 ◽  
Vol 31 (1) ◽  
pp. 89 ◽  
Author(s):  
Vedat Asil ◽  
Talat Körpınar ◽  
Essin Turhan
Keyword(s):  
Ricci Tensor ◽  
Three Dimensional ◽  
Kenmotsu Manifold ◽  
3 Dimensional ◽  
Developable Surfaces ◽  
Tangent Developable ◽  
Inextensible Flows ◽  
Parallel Ricci Tensor

In this paper, we study inextensible flows of tangent developable surfaces of biharmonic B-slant helices in the special three-dimensional Kenmotsu manifold K with η-parallel ricci tensor. We express some interesting relations about inextensible flows of this surfaces.

scholarly journals η-Ricci Solitons on Sasakian 3-Manifolds

2017 ◽  
Vol 55 (2) ◽  
pp. 143-156
Author(s):  
Pradip Majhi ◽  
Uday Chand De ◽  
Debabrata Kar
Keyword(s):  
Ricci Tensor ◽  
Ricci Soliton ◽  
Ricci Solitons ◽  
Conformally Flat ◽  
Curvature Condition ◽  
Cyclic Parallel Ricci Tensor ◽  
Codazzi Type ◽  
Parallel Ricci Tensor

AbstractIn this paper we studyη-Ricci solitons on Sasakian 3-manifolds. Among others we prove that anη-Ricci soliton on a Sasakian 3-manifold is anη-Einstien manifold. Moreover we considerη-Ricci solitons on Sasakian 3-manifolds with Ricci tensor of Codazzi type and cyclic parallel Ricci tensor. Beside these we study conformally flat andφ-Ricci symmetricη-Ricci soliton on Sasakian 3-manifolds. Alsoη-Ricci soliton on Sasakian 3-manifolds with the curvature conditionQ.R= 0 have been considered. Finally, we construct an example to prove the non-existence of properη-Ricci solitons on Sasakian 3-manifolds and verify some results.

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