scholarly journals On a New type of Tensor on Real Hypersurfaces in Non-Flat Complex Space Forms

Symmetry ◽  
2019 ◽  
Vol 11 (4) ◽  
pp. 559
Author(s):  
George Kaimakamis ◽  
Konstantina Panagiotidou
Keyword(s):  
Curvature Tensor ◽  
Complex Space ◽  
Three Dimensional ◽  
Real Hypersurfaces ◽  
Weyl Curvature ◽  
Space Forms ◽  
Hopf Hypersurfaces ◽  
Weyl Curvature Tensor ◽  
New Type ◽  
Complex Space Forms

In this paper the notion of ∗ -Weyl curvature tensor on real hypersurfaces in non-flat complex space forms is introduced. It is related to the ∗ -Ricci tensor of a real hypersurface. The aim of this paper is to provide two classification theorems concerning real hypersurfaces in non-flat complex space forms in terms of ∗ -Weyl curvature tensor. More precisely, Hopf hypersurfaces of dimension greater or equal to three in non-flat complex space forms with vanishing ∗ -Weyl curvature tensor are classified. Next, all three dimensional real hypersurfaces in non-flat complex space forms, whose ∗ -Weyl curvature tensor vanishes identically are classified. The used methods are based on tools from differential geometry and solving systems of differential equations.

scholarly journals CONFORMALLY OSSERMAN MANIFOLDS AND CONFORMALLY COMPLEX SPACE FORMS

2004 ◽  
Vol 01 (01n02) ◽  
pp. 97-106 ◽  
Author(s):  
N. BLAŽIĆ ◽  
P. GILKEY
Keyword(s):  
Curvature Tensor ◽  
Complex Space ◽  
Jacobi Operator ◽  
Space Forms ◽  
Conformal Curvature ◽  
Conformal Curvature Tensor ◽  
Weyl Curvature Tensor ◽  
Complex Space Forms ◽  
Weyl Conformal Curvature Tensor ◽  
Complex Projective

We characterize manifolds which are locally conformally equivalent to either complex projective space or to its negative curvature dual in terms of their Weyl curvature tensor. As a byproduct of this investigation, we classify the conformally complex space forms if the dimension is at least 8. We also study when the Jacobi operator associated to the Weyl conformal curvature tensor of a Riemannian manifold has constant eigenvalues on the bundle of unit tangent vectors and classify such manifolds which are not conformally flat in dimensions congruent to 2 mod 4.

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 On Three Dimensional Real Hypersurfaces in Complex Space Forms

2010 ◽  
Vol 33 (1) ◽  
pp. 31-47
Author(s):  
Jong Taek CHO ◽  
Tatsuyoshi HAMADA ◽  
Jun-ichi INOGUCHI
Keyword(s):  
Complex Space ◽  
Three Dimensional ◽  
Real Hypersurfaces ◽  
Space Forms ◽  
Complex Space Forms

A Classification of Three-dimensional Real Hypersurfaces in Non-flat Complex Space Forms in Terms of their Generalized Tanaka–Webster Lie Derivative

2016 ◽  
Vol 59 (4) ◽  
pp. 813-823
Author(s):  
George Kaimakamis ◽  
Konstantina Panagiotidou ◽  
Juan de Dios Perez
Keyword(s):  
Vector Field ◽  
Complex Space ◽  
Space Form ◽  
Three Dimensional ◽  
Real Hypersurfaces ◽  
Lie Derivative ◽  
Space Forms ◽  
Levi Civita Connection ◽  
Complex Space Forms

AbstractOn a real hypersurface M in a non-flat complex space form there exist the Levi–Civita and the k-th generalized Tanaka–Webster connections. The aim of this paper is to study three dimensional real hypersurfaces in non-flat complex space forms, whose Lie derivative of the structure Jacobi operatorwith respect to the Levi–Civita connection coincides with the Lie derivative of it with respect to the k-th generalized Tanaka-Webster connection. The Lie derivatives are considered in direction of the structure vector field and in direction of any vector field orthogonal to the structure vector field.

scholarly journals Commuting Conditions of the k-th Cho operator with the structure Jacobi operator of real hypersurfaces in complex space forms

2015 ◽  
Vol 13 (1) ◽  
Author(s):  
Konstantina Panagiotidou ◽  
Juan de Dios Pérez
Keyword(s):  
Vector Field ◽  
Hyperbolic Space ◽  
Complex Space ◽  
Jacobi Operator ◽  
Three Dimensional ◽  
Complex Hyperbolic Space ◽  
Real Hypersurfaces ◽  
Space Forms ◽  
Structure Jacobi Operator ◽  
Complex Space Forms

AbstractIn this paper three dimensional real hypersurfaces in non-flat complex space forms whose k-th Cho operator with respect to the structure vector field ξ commutes with the structure Jacobi operator are classified. Furthermore, it is proved that the only three dimensional real hypersurfaces in non-flat complex space forms, whose k-th Cho operator with respect to any vector field X orthogonal to structure vector field commutes with the structure Jacobi operator, are the ruled ones. Finally, results concerning real hypersurfaces in complex hyperbolic space satisfying the above conditions are also provided.

Sign in / Sign up

Export Citation Format

Share Document