scholarly journals Special lightlike hypersurfaces of indefinite Kaehler manifolds

Filomat ◽  
2016 ◽  
Vol 30 (7) ◽  
pp. 1919-1930 ◽  
Author(s):  
Dae Jin
Keyword(s):  
Complex Space ◽  
Space Form ◽  
Complex Space Form ◽  
Kaehler Manifold ◽  
Kaehler Manifolds ◽  
Almost Complex ◽  
Lightlike Hypersurfaces

In this paper, we define three types of lightlike hypersurfaces of an indefinite Kaehler manifold, which are called Hopf, recurrent and Lie recurrent lightlike hypersurfaces. After that we provide several new results on such three type lightlike hypersurfaces of an indefinite Kaehler manifold or an indefinite almost complex space form.

Einstein-Kaehler Manifolds Immersed in a Complex Projective Space

1976 ◽  
Vol 28 (1) ◽  
pp. 1-8 ◽  
Author(s):  
Hisao Nakaga
Keyword(s):  
Projective Space ◽  
Complex Projective Space ◽  
Complex Space ◽  
Space Form ◽  
Complex Space Form ◽  
Local Version ◽  
Kaehler Manifold ◽  
Kaehler Manifolds ◽  
Simply Connected ◽  
Complex Projective

A Kaehler manifold of constant holomorphic curvature is called a complex space form. By a Kaehler submanifold we mean a complex submanifold with the induced Kaehler metric. B. Smyth [5] has studied a complete Einstein- Kaehler hypersurface in a complete and simply connected complex space form and classified completely the hypersurface. The local version of this result has been shown to be true by S. S. Chern [1], and partially by T. Takahashi [6] independently.

scholarly journals On some inequalities for submanifolds of Bochner-Kaehler manifolds

Filomat ◽  
2017 ◽  
Vol 31 (18) ◽  
pp. 5511-5523
Author(s):  
Mehraj Lone ◽  
Mohammed Jamali ◽  
Mohammad Shahid
Keyword(s):  
Mean Curvature ◽  
Complex Space ◽  
Space Form ◽  
Real Space ◽  
Complex Space Form ◽  
Warping Function ◽  
Kaehler Manifold ◽  
Kaehler Manifolds

Chen established sharp inequalities between certain Riemannian invariants and the squared norm of mean curvature for submanifolds in real space form as well as in complex space form. In this paper we generalize Chen inequalities for submanifolds of Bochner-Kaehler manifolds. Moreover, we study CRwarped product submanifolds of Bochner-Kaehler manifold and establish an inequality for the Laplacian of the warping function, from which we conclude some obstructions to the existence of such immersions.

scholarly journals OnCR-Lightlike Product of an Indefinite Kaehler Manifold

2011 ◽  
Vol 2011 ◽  
pp. 1-10 ◽  
Author(s):  
Rakesh Kumar ◽  
Jasleen Kaur ◽  
R. K. Nagaich
Keyword(s):  
Euclidean Space ◽  
Complex Space ◽  
Space Form ◽  
Complex Space Form ◽  
Kaehler Manifold ◽  
Lightlike Submanifolds ◽  
Lightlike Submanifold

We have studied mixed foliateCR-lightlike submanifolds andCR-lightlike product of an indefinite Kaehler manifold and also obtained relationship between them. Mixed foliateCR-lightlike submanifold of indefinite complex space form has also been discussed and showed that the indefinite Kaehler manifold becomes the complex semi-Euclidean space.

scholarly journals CR-warped product submanifolds of a generalized complex space form

2017 ◽  
Vol 4 (1) ◽  
pp. 1306153
Author(s):  
Meraj Ali Khan ◽  
Amira A. Ishan ◽  
Hari M. Srivastava
Keyword(s):  
Warped Product ◽  
Complex Space ◽  
Space Form ◽  
Complex Space Form ◽  
Generalized Complex

On a Characterization of Real Hypersurfaces of Type a in a Complex Space Form

1994 ◽  
Vol 37 (2) ◽  
pp. 238-244 ◽  
Author(s):  
U-Hang Ki ◽  
Young-Jin Suh
Keyword(s):  
Complex Space ◽  
Space Form ◽  
Type A ◽  
Complex Space Form ◽  
Real Hypersurfaces ◽  
Orthogonal Distribution

AbstractIn this paper, under certain conditions on the orthogonal distribution T0, we give a characterization of real hypersurfaces of type A in a complex space form Mn(c), c ≠ 0.

scholarly journals Quasi-Einstein Hypersurfaces of Complex Space Forms

2020 ◽  
Vol 2020 ◽  
pp. 1-9
Author(s):  
Xiaomin Chen ◽  
Xuehui Cui
Keyword(s):  
Real Hypersurface ◽  
Complex Space ◽  
Space Form ◽  
Ricci Soliton ◽  
Complex Space Form ◽  
Einstein Metric ◽  
Space Forms ◽  
The Real ◽  
Complex Euclidean Space ◽  
Complex Space Forms

Based on a well-known fact that there are no Einstein hypersurfaces in a nonflat complex space form, in this article, we study the quasi-Einstein condition, which is a generalization of an Einstein metric, on the real hypersurface of a nonflat complex space form. For the real hypersurface with quasi-Einstein metric of a complex Euclidean space, we also give a classification. Since a gradient Ricci soliton is a special quasi-Einstein metric, our results improve some conclusions of Cho and Kimura.

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