• 대한수학회논문집
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• 제27권2호
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• pp.297-306
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• 2012

In this paper we study (${\epsilon}$)-Lorentzian para-Sasakian manifolds and show its existence by an example. Some basic results regarding such manifolds have been deduced. Finally, we study conformally flat and Weyl-semisymmetric (${\epsilon}$)-Lorentzian para-Sasakian manifolds.

• 대한수학회논문집
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• 제39권2호
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• pp.493-511
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• 2024

We introduce invariant rigged null hypersurfaces of indefinite almost contact manifolds, by paying attention to those of indefinite nearly α-Sasakian manifolds. We prove that, under some conditions, there exist leaves of the integrable screen distribution of the ambient manifolds admitting nearly α-Sasakian structures.

• Kyungpook Mathematical Journal
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• 제61권3호
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• pp.645-660
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• 2021

This paper examines the behavior of a 3-dimensional trans-Sasakian manifold equipped with a gradient generalized quasi-Yamabe soliton. In particular, It is shown that α-Sasakian, β-Kenmotsu and cosymplectic manifolds satisfy the gradient generalized quasi-Yamabe soliton equation. Furthermore, in the particular case when the potential vector field ζ of the quasi-Yamabe soliton is of gradient type ζ = grad(ψ), we derive a Poisson's equation from the quasi-Yamabe soliton equation. Also, we study harmonic aspects of quasi-Yamabe solitons on 3-dimensional trans-Sasakian manifolds sharing a harmonic potential function ψ. Finally, we observe that 3-dimensional compact trans-Sasakian manifold admits the gradient generalized almost quasi-Yamabe soliton with Hodge-de Rham potential ψ. This research ends with few examples of quasi-Yamabe solitons on 3-dimensional trans-Sasakian manifolds.

• Korean Journal of Mathematics
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• 제27권3호
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• pp.793-801
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• 2019

The aim of the present paper is to study certain recurrent properties of LP-Sasakian manifolds. Here we first describe Ricci ${\eta}$-recurrent LP-Sasakian manifolds. Further we study semi-generalized recurrent and three dimensional locally generalized concircularly ${\phi}$-recurrent LP-Sasakian manifolds and got interesting results.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제8권2호
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• pp.101-125
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• 2001

This is a survey article on almost Lorentzian paracontact manifolds. The study of Lorentsian almost paracontact manifolds was initiated by Matsumoto [On Lorentzian paracontact manifolds, Bull. Yamagata Univ. Nat. Sci. 12 (1989), 151-l56]. Later on several authors studied Lorentzian almost paracontact manifolds and their different classes, viz. LP-Sasakian and LSP-Sasakian manifolds. Different types of submanifolds, for example invariant, semi-invariant and almost semi-invariant, of Lorentzian almost paracontact manifold have been studied. Here, we present a brief survey of results on Lorentzian almost paracontact manifolds with their different classes and their different kind of submanifolds.

• Kyungpook Mathematical Journal
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• 제57권4호
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• pp.677-682
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• 2017

In this paper, we show that a Sasakian manifold which also satisfies the generalised gradient Ricci soliton equation, satisfying some conditions, is necessarily Einstein.

• Kyungpook Mathematical Journal
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• 제61권2호
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• pp.395-408
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• 2021

The object of the present paper is to study f-biharmonic submanifolds of three dimensional trans-Sasakian manifolds. We find some necessary and sufficient conditions for such submanifolds to be f-biharmonic.

• Korean Journal of Mathematics
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• 제29권2호
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• pp.425-434
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• 2021

The object of the present paper is to deduce some important results on generic submanifolds and generic product of trans-Sasakian manifolds with concurrent vector fields.

• 대한수학회논문집
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• 제23권1호
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• pp.95-110
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• 2008

The object of the present paper is to provide the existence of LP-Sasakian manifolds with $\eta$-recurrent, $\eta$-parallel, $\phi$-recurrent, $\phi$-parallel Ricci tensor with several non-trivial examples. Also generalized Ricci recurrent LP-Sasakian manifolds are studied with the existence of various examples.

• 대한수학회논문집
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• 제36권2호
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• pp.361-375
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• 2021

The object of the present paper is to deduce some important results on generic submanifolds and also generic product of LP-Sasakian manifolds with concurrent vector fields. Also, we provide a necessary and sufficient condition for which the invariant distribution D and anti-invariant distribution D^⊥ of M are Einstein. Also, we deduce an interesting necessary and sufficient condition for submanifolds of LP-Sasakian manifolds to be totally umbilical submanifolds. Especially we deal with the generic submanifolds admitting a Ricci soliton in LP-Sasakian manifolds endowed with concurrent vector fields.