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Journal Article•DOI•

Generalised CR-submanifolds of a LP-sasakian manifolds

Gopal Ghosh, Chiranjib Dey
01 Jan 2018-Filomat (National Library of Serbia)-Vol. 32, Iss: 18, pp 6281-6287
TL;DR: In this paper, the authors studied generalised CR-submanifolds of a LP-Sasakian manifold and showed that they can be constructed on a Kaehler manifold.
Abstract: The study of CR-submanifolds of a Kaehler manifold was initiated by Bejancu [1]. Since then many papers have appeared on CR-submanifolds. The aim of the present paper is to study generalised CR-submanifolds of a LP-Sasakian manifolds.

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Citations
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Journal Article•DOI•
Generalised CR -submanifolds of an (, ) -trans-Sasakian manifold with certain connection

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Mohd Danish Siddiqi, Janardan Parsad Ojha, Mobin Ahmad
01 Jan 2014-IOSR Journal of Mathematics
TL;DR: In this paper, integrability conditions of the distributions on generalised CR -submanifolds of an ), (   -trans-Sasakian manifolds with semi-symmetric non-moetric connection and geometry of leaves with semiautomated non-metric connection are studied.
Abstract: In this paper, generalised CR -submanifolds of an ) , (   -trans-Sasakian manifolds with semi-symmetric non-moetric connection are studied. Moreover, integrability conditions of the distributions on generalised CR -submanifolds of an ) , (   -trans-Sasakian manifolds with semi-symmetric non-moetric connection and geometry of leaves with semi-symmetric non-metric connection have been discussed. 2000 Mathematical Subject Classification :53C21, 53C25, 53C05.

3 citations

References
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Journal Article•DOI•
submanifolds of a Kaehler manifold. I

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Aurel Bejancu
01 Jan 1978
TL;DR: In this paper, the existence of totally umbilical proper CR submanifolds in an elliptic or hyperbolic complex space is proven. And the differential geometry of CR submansifolds of a Kaehler manifold is studied.
Abstract: The differential geometry of CR submanifolds of a Kaehler manifold is studied. Theorems on parallel normal sections and on a special type of flatness of the normal connection on a CR submanifold are obtained. Also, the nonexistence of totally umbilical proper CR submanifolds in an elliptic or hyperbolic complex space is proven.

206 citations

"Generalised CR-submanifolds of a LP..." refers methods in this paper

  • ...The study of CR-submanifolds of a Kaehler manifold was initiated by Bejancu [1]....

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On Lorentzian Paracontact Manifolds

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Koji Matsumoto
20 Jan 1989

139 citations

"Generalised CR-submanifolds of a LP..." refers background in this paper

  • ...Then such a structure (φ, ξ, η, 1) is termed as Lorentzian almost paracontact structure and the manifold with the structure (φ, ξ, η, 1) is called a Lorentzian almost paracontact manifold [9]....

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  • ...In the Lorentzian almost paracontact manifold M, the following relations hold [9]:...

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  • ...In an LP-Sasakian manifold M with the structure (φ, ξ, η, 1), it is easily seen that [9] ∇Xξ = φX, (6) (∇Xη)(Y) = 1(φX,Y) = (∇Yη)(X)....

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  • ...Matsumoto [9] introduced the notion of LP-Sasakian manifolds or in short LP-Sasakian manifolds....

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  • ...A Lorentzian almost paracontact manifold M endowed with the structure (φ, ξ, η, 1) is called an LPSasakian manifold [9] if (∇Xφ)Y = 1(φX, φY)ξ + η(Y)φ2X, (5) where ∇ denotes the operator of covariant differentiation with respect to the Lorentzian metric 1....

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Journal Article•
$zeta$-null geodesic gradient vector fields on a lorentzian para-sasakian manifold

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Koji Matsumoto, Ion Mihai, Radu Rosca
01 Jan 1995-Journal of The Korean Mathematical Society
TL;DR: In this article, a Lorentzian para-Sasakian manifold M$(varphi, \zeta, \eta, g)$ (abr. LPS-manifold) has been defined and studied.
Abstract: A Lorentzian para-Sasakian manifold M$(\varphi, \zeta, \eta, g)$ (abr. LPS-manifold) has been defined and studied in [9] and [10]. On the other hand, para-Sasakian (abr. PS)-manifolds are special semi-cosympletic manifolds (in the sense of [2]), that is, they are endowed with an almost cosympletic 2-form $\Omega$ such that $d^{2\eta}\Omega = \psi(d^\omega$ denotes the cohomological operator [6]), where the 3-form $\psi$ is the associated Lefebvre form of $\Omega$ ([8]). If $\eta$ is exact, $\psi$ is a $d^{2\eta}$-exact form, the manifold M is called an exact Ps-manifold. Clearly, any LPS-manifold is endowed with a semi-cosymplectic structure (abr. SC-structure).

29 citations

"Generalised CR-submanifolds of a LP..." refers methods in this paper

  • ...An example of a five dimensional LP-Sasakian manifold was given by Matsumoto, Mihai and Rosaca in [10]....

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Semi-Invariant Submanifolds of a Lorentzian Para-Sasakian Manifold

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B. S. R. V. Prasad
01 Jan 1998
TL;DR: In this paper, the integrability condition of the distribution on semi-invariant submanifolds of LP-Sasakian manifold is studied, where the authors consider the Lorentzian para contact structure.
Abstract: Recently Matsumoto (1) introduced the idea of Lorentzian para contact structure and studied its several properties. In the present paper we studied the integrability condition of the distribution on semi-invariant submanifolds of LP-Sasakian manifold. p p p

22 citations

"Generalised CR-submanifolds of a LP..." refers background in this paper

  • ...Prasad [4], Prasad and Ojha [15] studied submanifolds of a LP-Sasakian manifolds....

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LP-sasakian manifolds with quasi-conformal curvature tensor

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Uday Chand De
01 Jan 2013
TL;DR: In this article, a Sasakian manifold with quasi-conformal curvature tensors was studied and the object of the paper was to study the curvatures of the manifold.
Abstract: The object of the paper is to study a Sasakian manifold with quasi-conformal curvature tensor.

16 citations

"Generalised CR-submanifolds of a LP..." refers background in this paper

  • ...LP-Sasakian manifolds have been studied by several authors such as ([11], [6], [2]) and many others....

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Generalised CR -submanifolds of an (, ) -trans-Sasakian manifold with certain connection

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Mohd Danish Siddiqi, Janardan Parsad Ojha, Mobin Ahmad
Generic submanifolds of Sasakian manifolds

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