GCR-Lightlike Product of Indefinite Kaehler Manifolds

Kaehler Manifolds ◽

Lightlike Submanifolds ◽

We study geodesic -lightlike submanifolds of indefinite Kaehler manifolds and obtain some necessary and sufficient conditions for a -lightlike submanifold to be a -lightlike product.

Integrability of distributions in CR-lightlike submanifolds

Tamkang Journal of Mathematics ◽

10.5556/j.tkjm.33.2002.209-222 ◽

2002 ◽

Vol 33 (3) ◽

pp. 209-222

Author(s):

Bayram Sahin ◽

Rifat Gunes

Keyword(s):

Sufficient Conditions ◽

Kaehler Manifold ◽

Kaehler Manifolds ◽

Lightlike Submanifolds ◽

In this paper, we study CR-lighlike submanifolds of an indefinite Kaehler manifold. Integrability of distributions on CR-lightlike submanifold investigated. We give some necessary and sufficient conditions on integrability of distibutions on CR-lightlike submanifolds in an indefinite Kaehler manifolds.

Some results on normal GCR-lightlike submanifolds of indefinite nearly Kaehler manifolds

International Journal of Geometric Methods in Modern Physics ◽

10.1142/s0219887819500373 ◽

2019 ◽

Vol 16 (03) ◽

pp. 1950037

Author(s):

Megha ◽

Sangeet Kumar

Keyword(s):

Sufficient Conditions ◽

Characterization Theorem ◽

Kaehler Manifold ◽

Kaehler Manifolds ◽

Holomorphic Bisectional Curvature ◽

Nearly Kaehler Manifold ◽

Lightlike Submanifolds ◽

Lightlike Submanifold ◽

Normal Formula

The purpose of this paper is to study normal [Formula: see text]-lightlike submanifolds of indefinite nearly Kaehler manifolds. We find some necessary and sufficient conditions for an isometrically immersed [Formula: see text]-lightlike submanifold of an indefinite nearly Kaehler manifold to be a normal [Formula: see text]-lightlike submanifold. Further, we derive a characterization theorem for holomorphic bisectional curvature of a normal [Formula: see text]-lightlike submanifold of an indefinite nearly Kaehler manifold.

On the geometry of screen conformal submersions of semi-transversal lightlike submanifolds

Asian-European Journal of Mathematics ◽

10.1142/s1793557121501333 ◽

2020 ◽

pp. 2150133

Author(s):

Rupali Kaushal ◽

Rakesh Kumar ◽

Rakesh Kumar Nagaich

Keyword(s):

Sufficient Conditions ◽

Kaehler Manifolds ◽

Lightlike Submanifolds

We study screen conformal lightlike submersions of semi-transversal lightlike submanifolds of indefinite Kaehler manifolds, which can be considered as a lightlike version of horizontally conformal submersions. We establish necessary and sufficient conditions for a screen conformal lightlike submersion to be harmonic.

GCR-Lightlike Product of Indefinite Sasakian Manifolds

Advances in Mathematical Physics ◽

10.1155/2011/983069 ◽

2011 ◽

Vol 2011 ◽

pp. 1-12 ◽

Cited By ~ 5

Author(s):

Rakesh Kumar ◽

Varun Jain ◽

R. K. Nagaich

Keyword(s):

Sufficient Conditions ◽

Sasakian Manifolds ◽

Lightlike Submanifolds ◽

We study mixed geodesicGCR-lightlike submanifolds of indefinite Sasakian manifolds and obtain some necessary and sufficient conditions for aGCR-lightlike submanifold to be aGCR-lightlike product.

Slant lightlike submanifolds of indefinite Sasakian manifolds

Filomat ◽

10.2298/fil1202277s ◽

2012 ◽

Vol 26 (2) ◽

pp. 277-287 ◽

Cited By ~ 1

Author(s):

Bayram Sahin ◽

Cumali Yıldırım

Keyword(s):

Sufficient Conditions ◽

Sasakian Manifold ◽

Sasakian Manifolds ◽

Lightlike Submanifolds ◽

In this paper, we define and study both slant lightlike submanifolds and screen slant lightlike submanifolds of an indefinite Sasakian manifold. We provide non-trivial examples and obtain necessary and sufficient conditions for the existence of a slant lightlike submanifold.

On some types of lightlike submanifolds of golden semi-Riemannian manifolds

Filomat ◽

10.2298/fil1910231e ◽

2019 ◽

Vol 33 (10) ◽

pp. 3231-3242

Author(s):

Feyza Erdoğan

Keyword(s):

Riemannian Manifolds ◽

Sufficient Conditions ◽

Metric Connection ◽

Lightlike Submanifolds

The main purpose of the present paper is to study the geometry of screen transversal lightlike submanifolds and radical screen transversal lightlike submanifolds and screen transversal anti-invariant lightlike submanifolds of Golden semi-Riemannian manifolds. We investigate the geometry of distributions and obtain necessary and sufficient conditions for the induced connection on these manifolds to be metric connection. We also obtain characterizations of screen transversal anti-invariant lightlike submanifolds of Golden semi-Riemannian manifolds. Finally, we give two examples.

Radical screen transversal lightlike submanifolds of indefinite Kaehler manifolds admitting a quarter-symmetric non-metric connection

International Journal of Geometric Methods in Modern Physics ◽

10.1142/s021988781850024x ◽

2018 ◽

Vol 15 (02) ◽

pp. 1850024

Author(s):

Garima Gupta ◽

Rakesh Kumar ◽

Rakesh Kumar Nagaich

Keyword(s):

Product Manifold ◽

Necessary And Sufficient Condition ◽

Kaehler Manifold ◽

Screen Distribution ◽

Kaehler Manifolds ◽

Metric Connection ◽

Characterization Theorems ◽

Lightlike Submanifolds ◽

We study radical screen transversal ([Formula: see text])-lightlike submanifolds of an indefinite Kaehler manifold admitting a quarter-symmetric non-metric connection and obtain a necessary and sufficient condition for the screen distribution of a radical [Formula: see text]-lightlike submanifold to be integrable. We also study totally umbilical radical [Formula: see text]-lightlike submanifolds and obtain some characterization theorems for a radical [Formula: see text]-lightlike submanifold to be a lightlike product manifold. Finally, we establish some results regarding the vanishes of null sectional curvature.

Geometry of semi-transversal lightlike warped product submanifolds of indefinite Kaehler manifolds

Asian-European Journal of Mathematics ◽

10.1142/s1793557121500017 ◽

2019 ◽

pp. 2150001

Author(s):

Sangeet Kumar

Keyword(s):

Warped Product ◽

Shape Operator ◽

Sufficient Condition ◽

Necessary And Sufficient Condition ◽

Kaehler Manifold ◽

Type Formula ◽

Kaehler Manifolds ◽

Lightlike Submanifolds ◽

In this paper, we investigate warped product semi-transversal lightlike submanifolds of indefinite Kaehler manifolds. It is shown that there does not exist any warped product semi-transversal lightlike submanifold of the type [Formula: see text] in an indefinite Kaehler manifold. Moreover, a necessary and sufficient condition for an isometrically immersed semi-transversal lightlike submanifold of an indefinite Kaehler manifold to be a semi-transversal lightlike warped product of the type [Formula: see text] is obtained, in terms of the shape operator.

Radical transversal SCR-lightlike submanifolds of indefinite Sasakian manifolds

Filomat ◽

10.2298/fil2108585s ◽

2021 ◽

Vol 35 (8) ◽

pp. 2585-2594

Author(s):

S.S. Shukla ◽

Akhilesh Yadav

Keyword(s):

Sufficient Conditions ◽

Characterization Theorem ◽

Sasakian Manifold ◽

Sasakian Manifolds ◽

Totally Geodesic ◽

Integrability Conditions ◽

Cauchy Riemann ◽

Lightlike Submanifolds

In this paper, we introduce the notion of radical transversal screen Cauchy-Riemann (SCR)- lightlike submanifolds of indefinite Sasakian manifolds giving characterization theorem with some nontrivial examples of such submanifolds. Integrability conditions of distributions D1, D2, D and D? on radical transversal SCR-lightlike submanifolds of an indefinite Sasakian manifold have been obtained. Further, we obtain necessary and sufficient conditions for foliations determined by above distributions to be totally geodesic.

The extinction time of a general birth and death process with catastrophes

Journal of Applied Probability ◽

10.1017/s0021900200116031 ◽

1986 ◽

Vol 23 (04) ◽

pp. 851-858 ◽

Cited By ~ 1

Author(s):

P. J. Brockwell

Keyword(s):

Laplace Transform ◽

Size Distribution ◽

Sufficient Conditions ◽

Death Process ◽

Extinction Time ◽

Birth And Death Process ◽

Different Types ◽

The Laplace Transform ◽

Necessary And Sufficient

The Laplace transform of the extinction time is determined for a general birth and death process with arbitrary catastrophe rate and catastrophe size distribution. It is assumed only that the birth rates satisfyλ0= 0,λj> 0 for eachj> 0, and. Necessary and sufficient conditions for certain extinction of the population are derived. The results are applied to the linear birth and death process (λj=jλ, µj=jμ) with catastrophes of several different types.