3-Dimensional real hypersurfaces with transversal $\eta$-Killing Ricci tensor field of a complex space form

2020 ◽  
Vol 44 (1) ◽  
pp. 203-211
Author(s):  
Mayuko Kon
Keyword(s):  
Ricci Tensor ◽  
Tensor Field ◽  
Complex Space ◽  
Space Form ◽  
Complex Space Form ◽  
Real Hypersurfaces ◽  
3 Dimensional

scholarly journals On pseudo-Einstein real hypersurfaces

2020 ◽  
Vol 20 (4) ◽  
pp. 559-571
Author(s):  
Mayuko Kon
Keyword(s):  
Ricci Tensor ◽  
Real Hypersurface ◽  
Vector Fields ◽  
Complex Space ◽  
Space Form ◽  
Complex Space Form ◽  
Real Hypersurfaces ◽  
Definition Of ◽  
Weaker Conditions

AbstractLet M be a real hypersurface of a complex space form Mn(c) with c ≠ 0 and n ≥ 3. We show that the Ricci tensor S of M satisfies S(X, Y) = ag(X, Y) for all vector fields X and Y on the holomorphic distribution, a being a constant, if and only if M is a pseudo-Einstein real hypersurface. By doing this we can give the definition of pseudo-Einstein real hypersurface under weaker conditions.

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.

A Characterization of Real Hypersurfaces in Complex Space Forms in Terms of the Ricci Tensor

1997 ◽  
Vol 40 (3) ◽  
pp. 257-265 ◽  
Author(s):  
Christos Baikoussis
Keyword(s):  
Ricci Tensor ◽  
Complex Space ◽  
Space Form ◽  
Complex Space Form ◽  
Real Hypersurfaces ◽  
Space Forms ◽  
Complex Space Forms ◽  
Orthogonal Distribution

AbstractWe study real hypersurfaces of a complex space form Mn(c), c ≠ 0 under certain conditions of the Ricci tensor on the orthogonal distribution T0.

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