• Bulletin of the Korean Mathematical Society
• /
• v.51 no.6
• /
• pp.1711-1726
• /
• 2014

In this paper, we study the geometry of indefinite generalized Sasakian space form $\bar{M}(f_1,f_2,f_3)$ admitting a generic lightlike submanifold M subject such that the structure vector field of $\bar{M}(f_1,f_2,f_3)$ is tangent to M. The purpose of this paper is to prove a classification theorem of such an indefinite generalized Sasakian space form.

• Kyungpook Mathematical Journal
• /
• v.55 no.4
• /
• pp.1097-1104
• /
• 2015

In this paper, we study the geometry of indefinite generalized Sasakian space form $\bar{M}(f_1,f_2,f_3)$ admitting a lightlike hypersurface M subject such that the almost contact structure vector field ${\zeta}$ of $\bar{M}(f_1,f_2,f_3)$ is tangent to M. We prove a classification theorem of such an indefinite generalized Sasakian space form.

• Kyungpook Mathematical Journal
• /
• v.62 no.4
• /
• pp.715-728
• /
• 2022

The aim of this article is to study the h-almost Ricci solitons and h-almost gradient Ricci solitons on generalized Sasakian-space-forms. First, we consider h-almost Ricci soliton with the potential vector field V as a contact vector field on generalized Sasakian-space-form of dimension greater than three. Next, we study h-almost gradient Ricci solitons on a three-dimensional quasi-Sasakian generalized Sasakian-space-form. In both the cases, several interesting results are obtained.

• Journal of the Korean Mathematical Society
• /
• v.60 no.2
• /
• pp.341-358
• /
• 2023

Our aim is to study the properties of Fischer-Marsden conjecture and Ricci-Bourguignon solitons within the framework of generalized Sasakian-space-forms with 𝛽-Kenmotsu structure. It is proven that a (2n + 1)-dimensional generalized Sasakian-space-form with 𝛽-Kenmotsu structure satisfying the Fischer-Marsden equation is a conformal gradient soliton. Also, it is shown that a generalized Sasakian-space-form with 𝛽-Kenmotsu structure admitting a gradient Ricci-Bourguignon soliton is either ψ∖T^k × M^2n+1-k or gradient 𝜂-Yamabe soliton.

• Honam Mathematical Journal
• /
• v.45 no.2
• /
• pp.215-230
• /
• 2023

In this article, generalized Sasakian space forms are investigated on W₀ -curvature tensor. Characterizations of generalized Sasakian space forms are obtained on W₀-curvature tensor. Special curvature conditions established with the help of Riemann, Ricci, concircular, projective curvature tensors are discussed on W₀-curvature tensor. With the help of these curvature conditions, important characterizations of generalized Sasakian space forms are obtained. In addition, the concepts of W₀-pseudosymmetry and W₀ -Ricci pseudosymmetry are defined and the behavior according to these concepts for the generalized Sasakian space form is examined.

• Journal of the Chungcheong Mathematical Society
• /
• v.33 no.4
• /
• pp.375-386
• /
• 2020

In this article we have studied different types of symmetricness of trans-Sasakian space forms.

• East Asian mathematical journal
• /
• v.33 no.5
• /
• pp.533-542
• /
• 2017

We study the geometry of indefinite trans-Sasakian manifold ${\bar{M}}$ admitting a half lightlike submanifold M such that the structure vector field of ${\bar{M}}$ belongs to the transversal vector bundle of M. We prove several classification theorems of such an indefinite trans-Sasakian manifold.

• Honam Mathematical Journal
• /
• v.35 no.4
• /
• pp.657-666
• /
• 2013

We study indefinite trans-Sasakian manifold $\bar{M}$ admitting an ascreen lightlike hypersurface M. Our main results are several classification theorems of such an indefinite trans-Sasakian manifold.

• Communications of the Korean Mathematical Society
• /
• v.31 no.3
• /
• pp.613-624
• /
• 2016

We define a new connection on a semi-Riemannian manifold. Its notion contains two well known notions; (1) semi-symmetric connection and (2) quarter-symmetric connection. In this paper, we study the geometry of lightlike hypersurfaces of an indefinite generalized Sasakian space form with a symmetric metric connection of type (${\ell}$, m).

• Communications of the Korean Mathematical Society
• /
• v.34 no.4
• /
• pp.1315-1328
• /
• 2019

The object of the present paper is to study ${\eta}$-recurrent ${\ast}$-Ricci tensor, ${\ast}$-Ricci semisymmetric and globally ${\varphi}-{\ast}$-Ricci symmetric contact metric generalized (${\kappa}$, ${\mu}$)-space form. Besides these, ${\ast}$-Ricci soliton and gradient ${\ast}$-Ricci soliton in contact metric generalized (${\kappa}$, ${\mu}$)-space form have been studied.