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ON 3-DIMENSIONAL LORENTZIAN CONCIRCULAR STRUCTURE MANIFOLDS
Chaubey, Sudhakar Kumar,Shaikh, Absos Ali Korean Mathematical Society 2019 대한수학회논문집 Vol.34 No.1
The aim of the present paper is to study the Eisenhart problems of finding the properties of second order parallel tensors (symmetric and skew-symmetric) on a 3-dimensional LCS-manifold. We also investigate the properties of Ricci solitons, Ricci semisymmetric, locally ${\phi}$-symmetric, ${\eta}$-parallel Ricci tensor and a non-null concircular vector field on $(LCS)_3$-manifolds.
Sudhakar Kumar Chaubey,서영진 대한수학회 2023 대한수학회지 Vol.60 No.2
Our aim is to study the properties of Fischer-Marsden conjecture and Ricci-Bourguignon solitons within the framework of generalized Sasakian-space-forms with $\beta$-Kenmotsu structure. It is proven that a $(2n+1)$-dimensional generalized Sasakian-space-form with $\beta$-Kenmotsu structure satisfying the Fischer-Marsden equation is a conformal gradient soliton. Also, it is shown that a generalized Sasakian-space-form with $\beta$-Kenmotsu structure admitting a gradient Ricci-Bourguignon soliton is either $\Psi \backslash T^{k} \times M^{2n+1-k}$ or gradient $\eta$-Yamabe soliton.
CERTAIN RESULTS ON SUBMANIFOLDS OF GENERALIZED SASAKIAN SPACE-FORMS
( Sunil Kumar Yadav ),( Sudhakar K Chaubey ) 호남수학회 2020 호남수학학술지 Vol.42 No.1
The object of the present paper is to study certain geometrical properties of the submanifolds of generalized Sasakian space-forms. We deduce some results related to the invariant and anti-invariant slant submanifolds of the generalized Sasakian space-forms. Finally, we study the properties of the sectional curvature, totally geodesic and umbilical submanifolds of the generalized Sasakian space-forms. To prove the existence of almost semiinvariant and anti-invariant submanifolds, we provide the non-trivial examples.
Siddiqi, Mohammed Danish,Chaubey, Sudhakar Kumar,Ramandi, Ghodratallah Fasihi Department of Mathematics 2021 Kyungpook mathematical journal Vol.61 No.3
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.
STUDY OF P-CURVATURE TENSOR IN THE SPACE-TIME OF GENERAL RELATIVITY
( Ganesh Prasad Pokhariyal ),( Sudhakar Kumar Chaubey ) 호남수학회 2023 호남수학학술지 Vol.45 No.2
The P-curvature tensor has been studied in the space-time of general relativity and it is found that the contracted part of this tensor vanishes in the Einstein space. It is shown that Rainich conditions for the existence of non-null electro variance can be obtained by P<sub>αβ</sub>. It is established that the divergence of tensor G<sub>αβ</sub> defined with the help of P<sub>αβ</sub> and scalar P is zero, so that it can be used to represent Einstein field equations. It is shown that for V4 satisfying Einstein like field equations, the tensor P<sub>αβ</sub> is conserved, if the energy momentum tensor is Codazzi type. The space-time satisfying Einstein’s field equations with vanishing of P-curvature tensor have been considered and existence of Killing, conformal Killing vector fields and perfect fluid space-time has been established.
Quasi hemi-slant submanifolds of cosymplectic manifolds
Rajendra Prasad,Sandeep Kumar Verma,Sumeet Kumar,Sudhakar K Chaubey 강원경기수학회 2020 한국수학논문집 Vol.28 No.2
We introduce and study quasi hemi-slant submanifolds of almost contact metric manifolds (especially, cosymplectic manifolds) and validate its existence by providing some non-trivial examples. Necessary and sufficient conditions for integrability of distributions, which are involved in the definition of quasi hemi-slant submanifolds of cosymplectic manifolds, are obtained. Also, we investigate the necessary and sufficient conditions for quasi hemi-slant submanifolds of cosymplectic manifolds to be totally geodesic and study the geometry of foliations determined by the distributions.
η-Einstein Solitons on (ε)-Kenmotsu Manifolds
MOHD. DANISH SIDDIQI,Sudhakar Kumar Chaubey 경북대학교 자연과학대학 수학과 2020 Kyungpook mathematical journal Vol.60 No.4
The objective of this study is to investigate η-Einstein solitons on (ε)-Kenmotsu manifolds when the Weyl-conformal curvature tensor satisfies some geometric properties such as being flat, semi-symmetric and Einstein semi-symmetric. Here, we discuss the properties of η-Einstein solitons on φ-symmetric (ε)-Kenmotsu manifolds.
h-almost Ricci Solitons on Generalized Sasakian-space-forms
Doddabhadrappla Gowda, Prakasha,Amruthalakshmi Malleshrao, Ravindranatha,Sudhakar Kumar, Chaubey,Pundikala, Veeresha,Young Jin, Suh Department of Mathematics 2022 Kyungpook mathematical journal Vol.62 No.4
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.