The Bochner type curvature tensor of pseudo-convexC R-structures on real hypersurfaces in complex space forms

1998 ◽  
Vol 63 (1-2) ◽  
pp. 134-146 ◽  
Author(s):  
Paola Matzeu ◽  
Vasile Oproiu
Keyword(s):  
Curvature Tensor ◽  
Complex Space ◽  
Real Hypersurfaces ◽  
Space Forms ◽  
Complex Space Forms

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.

On real hypersurfaces with  -parallel curvature tensor in complex space forms

2003 ◽  
Vol 101 (1/2) ◽  
pp. 1-12 ◽  
Author(s):  
J. G. Lee ◽  
J. D. Pérez, J. D. ◽  
Y. J. Suh
Keyword(s):  
Curvature Tensor ◽  
Complex Space ◽  
Real Hypersurfaces ◽  
Space Forms ◽  
Complex Space Forms

Some new results on real hypersurfaces with generalized Tanaka-Webster connection

2019 ◽  
Vol 69 (3) ◽  
pp. 665-674
Author(s):  
Wenjie Wang ◽  
Ximin Liu
Keyword(s):  
Real Hypersurface ◽  
Complex Space ◽  
Shape Operator ◽  
Real Hypersurfaces ◽  
Space Forms ◽  
Complex Dimension ◽  
Nonflat Complex Space Forms ◽  
Complex Space Forms ◽  
Ruled Real Hypersurface

Abstract Let M be a real hypersurface in nonflat complex space forms of complex dimension two. In this paper, we prove that the shape operator of M is transversally Killing with respect to the generalized Tanaka-Webster connection if and only if M is locally congruent to a type (A) or (B) real hypersurface. We also prove that shape operator of M commutes with Cho operator on holomorphic distribution if and only if M is locally congruent to a ruled real hypersurface.

Derivatives on Real Hypersurfaces of Two-Dimensional Non-flat Complex Space Forms

2017 ◽  
Vol 14 (2) ◽  
Author(s):  
George Kaimakamis ◽  
Konstantina Panagiotidou ◽  
Juan de Dios Pérez
Keyword(s):  
Complex Space ◽  
Real Hypersurfaces ◽  
Two Dimensional ◽  
Space Forms ◽  
Complex Space Forms

scholarly journals Ruled real hypersurfaces of complex space forms

2010 ◽  
Vol 33 (1) ◽  
pp. 123-134 ◽  
Author(s):  
Tatsuyoshi Hamada ◽  
Jun-ichi Inoguchi
Keyword(s):  
Complex Space ◽  
Real Hypersurfaces ◽  
Space Forms ◽  
Ruled Real Hypersurfaces ◽  
Complex Space Forms

scholarly journals The structure Jacobi operator of three-dimensional real hypersurfaces in non-flat complex space forms

2016 ◽  
Vol 39 (1) ◽  
pp. 154-174
Author(s):  
George Kaimakamis ◽  
Konstantina Panagiotidou ◽  
Juan de Dios Pérez
Keyword(s):  
Complex Space ◽  
Jacobi Operator ◽  
Three Dimensional ◽  
Real Hypersurfaces ◽  
Space Forms ◽  
Structure Jacobi Operator ◽  
Complex Space Forms
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