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.

Some characterization theorems on holomorphic sectional curvature of GCR-lightlike submanifolds

2017 ◽  
Vol 14 (03) ◽  
pp. 1750034 ◽  
Author(s):  
Varun Jain ◽  
Rachna Rani ◽  
Rakesh Kumar ◽  
R. K. Nagaich
Keyword(s):  
Sectional Curvature ◽  
Sasakian Manifold ◽  
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 a GCR-lightlike submanifold of an indefinite Sasakian manifold and obtain some characterization theorems on 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.

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.

Explicit construction of Lagrangian isometric immersion of a real-space-form Mn(c) into a complex-space-form M˜n(4c)

2002 ◽  
Vol 132 (3) ◽  
pp. 481-508 ◽  
Author(s):  
YUN MYUNG OH
Keyword(s):  
Sectional Curvature ◽  
Isometric Immersion ◽  
Complex Space ◽  
Space Form ◽  
Real Space ◽  
Constant Sectional Curvature ◽  
Complex Space Form ◽  
Product Decomposition ◽  
Twisted Product ◽  
Space Forms

In [4], it is proved that there exists a ‘unique’ adapted Lagrangian isometric immersion of a real-space-form Mn(c) of constant sectional curvature c into a complex-space-form M˜n(4c) of constant sectional curvature 4c associated with each twisted product decomposition of a real-space-form if its twistor form is twisted closed. Conversely, if L: Mn(c) → M˜n(4c) is a non-totally geodesic Lagrangian isometric immersion of a real-space-form Mn(c) into a complex-space-form M˜n(4c), then Mn(c) admits an appropriate twisted product decomposition with twisted closed twistor form and, moreover, the immersion L is determined by the corresponding adapted Lagrangian isometric immersion of the twisted product decomposition. It is natural to ask the explicit expressions of adapted Lagrangian isometric immersions of twisted product decompositions of real-space-forms Mn(c) into complex-space-forms M˜n(4c) for each case: c = 0, c > 0 and c < 0.

Some characterizations on minimal lightlike submanifolds

2017 ◽  
Vol 14 (07) ◽  
pp. 1750103 ◽  
Author(s):  
Sangeet Kumar
Keyword(s):  
Sectional Curvature ◽  
Ricci Tensor ◽  
Minimal Condition ◽  
Characterization Theorems ◽  
Lightlike Submanifolds ◽  
Lightlike Submanifold

The present paper deals with the study of minimal lightlike submanifolds. We investigate a class of lightlike submanifolds namely, generic lightlike submanifolds under the minimal condition. We give one nontrivial example for minimal generic lightlike submanifolds and derive some characterization theorems for a generic lightlike submanifold to be a minimal lightlike submanifold. We also establish some conditions for the distributions for generic lightlike submanifolds to be minimal. We further derive the expressions for sectional curvature, null sectional curvature and induced Ricci tensor for a minimal lightlike submanifold. Finally, we prove that for a minimal lightlike submanifold, the null sectional curvature vanishes and the induced Ricci tensor is symmetric.

scholarly journals PSEUDO-PARALLEL KAEHLERIAN SUBMANIFOLDS IN COMPLEX SPACE FORMS

2020 ◽  
pp. 321
Author(s):  
Ahmet Yildiz
Keyword(s):  
Sectional Curvature ◽  
Fundamental Form ◽  
Complex Space ◽  
Space Form ◽  
Dimensional Space ◽  
Second Fundamental Form ◽  
Holomorphic Sectional Curvature ◽  
Space Forms ◽  
Totally Geodesic ◽  
Complex Space Forms

Let $\tilde{M}^{m}(c)$ be a complex $m$-dimensional space form of holomorphic sectional curvature $c$ and $M^{n}$ be a complex $n$-dimensional Kaehlerian submanifold of $\tilde{M}^{m}(c).$ We prove that if $M^{n}$ is pseudo-parallel and $Ln-\frac{1}{2}(n+2)c\geqslant 0$ then $M$ $^{n}$ is totally geodesic. Also, we study Kaehlerian submanifolds of complex space form with recurrent second fundamental form.

scholarly journals Parallel submanifolds of complex space forms I

1983 ◽  
Vol 90 ◽  
pp. 85-117 ◽  
Author(s):  
Hiroo Naitoh
Keyword(s):  
Symmetric Space ◽  
Sectional Curvature ◽  
Complex Space ◽  
Space Form ◽  
Real Space ◽  
Hermitian Symmetric Space ◽  
Holomorphic Sectional Curvature ◽  
Space Forms ◽  
Simply Connected ◽  
Complex Space Forms

Complete parallel submanifolds of a real space form of constant sectional curvature k have been completely classified by Ferus [3] when k ≧ 0, and by Takeuchi [19] when k < 0. A complex space form is by definition a 2n-dimensional simply connected Hermitian symmetric space of constant holomorphic sectional curvature c and will be denoted by (c).

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