scholarly journals Screen transversal cauchy Riemann lightlike submanifolds

Filomat ◽  
2020 ◽  
Vol 34 (5) ◽  
pp. 1581-1599
Author(s):  
Burçin Doḡan ◽  
Bayram Şahin ◽  
Erol Yaşar
Keyword(s):  
Complex Space ◽  
Space Form ◽  
Complex Space Form ◽  
New Class ◽  
Metric Connection ◽  
Cauchy Riemann ◽  
Lightlike Submanifolds ◽  
Totally Real ◽  
Lightlike Submanifold

We introduce a new class of lightlike submanifolds, namely, Screen Transversal Cauchy Riemann (STCR)-lightlike submanifolds, of indefinite K?hler manifolds. We show that this new class is an umbrella of screen transversal lightlike, screen transversal totally real lightlike and CR-lightlike submanifolds. We give a few examples of a STCR lightlike submanifold, investigate the integrability of various distributions, obtain a characterization of such lightlike submanifolds in a complex space form and find new conditions for the induced connection to be a metric connection. Moreover, we investigate the existence of totally umbilical (STCR)-lightlike submanifolds and minimal (STCR)-lightlike submanifolds. The paper also contains several examples.

scholarly journals Characterization of Holomorphic Bisectional Curvature ofGCR-Lightlike Submanifolds

2012 ◽  
Vol 2012 ◽  
pp. 1-18 ◽  
Author(s):  
Sangeet Kumar ◽  
Rakesh Kumar ◽  
R. K. Nagaich
Keyword(s):  
Sectional Curvature ◽  
Complex Space ◽  
Space Form ◽  
Complex Space Form ◽  
Holomorphic Sectional Curvature ◽  
Bisectional Curvature ◽  
Holomorphic Bisectional Curvature ◽  
Characterization Theorems ◽  
Lightlike Submanifolds ◽  
Lightlike Submanifold

We obtain the expressions for sectional curvature, holomorphic sectional curvature, and holomorphic bisectional curvature of aGCR-lightlike submanifold of an indefinite Kaehler manifold. We discuss the boundedness of holomorphic sectional curvature ofGCR-lightlike submanifolds of an indefinite complex space form. We establish a condition for aGCR-lightlike submanifold of an indefinite complex space form to be null holomorphically flat. We also obtain some characterization theorems for holomorphic sectional and holomorphic bisectional curvature.

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.

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 Chen's problem on mixed foliate CR-submanifolds

1989 ◽  
Vol 40 (1) ◽  
pp. 157-160 ◽  
Author(s):  
Mohammed Ali Bashir
Keyword(s):  
Complex Space ◽  
Space Form ◽  
Complex Space Form ◽  
Complex Submanifold ◽  
Hyperbolic Complex ◽  
Real Submanifold ◽  
Totally Real Submanifold ◽  
Simply Connected ◽  
Totally Real ◽  
Cr Submanifolds

We prove that the simply connected compact mixed foliate CR-submanifold in a hyperbolic complex space form is either a complex submanifold or a totally real submanifold. This is the problem posed by Chen.

Totally real submanifolds in a generalized complex space form

2016 ◽  
Vol 10 (02) ◽  
pp. 1750035
Author(s):  
Majid Ali Choudhary
Keyword(s):  
Fundamental Form ◽  
Complex Space ◽  
Space Form ◽  
Second Fundamental Form ◽  
Text Structure ◽  
Complex Space Form ◽  
Real Submanifolds ◽  
Constant Length ◽  
Generalized Complex ◽  
Totally Real

In the present paper, we investigate totally real submanifolds in generalized complex space form. We study the [Formula: see text]-structure in the normal bundle of a totally real submanifold and derive some integral formulas computing the Laplacian of the square of the second fundamental form and using these formulas, we prove a pinching theorem. In fact, the purpose of this note is to generalize results proved in B. Y. Chen and K. Ogiue, On totally real manifolds, Trans. Amer. Math. Soc. 193 (1974) 257–266, S. S. Chern, M. Do Carmo and S. Kobayashi, Minimal submanifolds of a sphere with second fundamental form of constant length, in Functional Analysis and Related Fields (Springer-Verlag, 1970), pp. 57–75 to the case, when the ambient manifold is generalized complex space form.

scholarly journals Totally real submanifolds of a complex space form

1996 ◽  
Vol 19 (1) ◽  
pp. 39-44 ◽  
Author(s):  
U-Hang Ki ◽  
Young Ho Kim
Keyword(s):  
Mean Curvature ◽  
Complex Space ◽  
Space Form ◽  
Curvature Vector ◽  
Complex Space Form ◽  
Mean Curvature Vector ◽  
Parallel Mean Curvature Vector ◽  
Real Submanifolds ◽  
Parallel Mean Curvature ◽  
Totally Real

Totally real submanifolds of a complex space form are studied. In particular, totally real submanifolds of a complex number space with parallel mean curvature vector are classified.

scholarly journals Real hypersurfaces with constant totally real sectional curvature in a complex space form

2000 ◽  
Vol 50 (3) ◽  
pp. 531-537 ◽  
Author(s):  
Miguel Ortega ◽  
Juan de dios Pérez ◽  
Young Jin Suh
Keyword(s):  
Sectional Curvature ◽  
Complex Space ◽  
Space Form ◽  
Complex Space Form ◽  
Real Hypersurfaces ◽  
Totally Real
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