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Riemannian manifolds with a semi-symmetric metric $P$-connection
Sudhakar Kr Chaubey,이재원,Sunil Kr Yadav 대한수학회 2019 대한수학회지 Vol.56 No.4
We define a class of semi-symmetric metric connection on a Riemannian manifold for which the conformal, the projective, the concircular, the quasi conformal and the $m$-projective curvature tensors are invariant. We also study the properties of semisymmetric, Ricci semisymmetric and Eisenhart problems for solving second order parallel symmetric and skew-symmetric tensors on the Riemannian manifolds equipped with a semi-symmetric metric $P$-connection.
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.
RIEMANNIAN MANIFOLDS WITH A SEMI-SYMMETRIC METRIC P-CONNECTION
Chaubey, Sudhakar Kr,Lee, Jae Won,Yadav, Sunil Kr Korean Mathematical Society 2019 대한수학회지 Vol.56 No.4
We define a class of semi-symmetric metric connection on a Riemannian manifold for which the conformal, the projective, the concircular, the quasi conformal and the m-projective curvature tensors are invariant. We also study the properties of semisymmetric, Ricci semisymmetric and Eisenhart problems for solving second order parallel symmetric and skew-symmetric tensors on the Riemannian manifolds equipped with a semi-symmetric metric P-connection.
KENMOTSU MANIFOLDS SATISFYING THE FISCHER-MARSDEN EQUATION
Chaubey, Sudhakar Kr,De, Uday Chand,Suh, Young Jin Korean Mathematical Society 2021 대한수학회지 Vol.58 No.3
The present paper deals with the study of Fischer-Marsden conjecture on a Kenmotsu manifold. It is proved that if a Kenmotsu metric satisfies 𝔏<sup>*</sup><sub>g</sub>(λ) = 0 on a (2n + 1)-dimensional Kenmotsu manifold M<sup>2n+1</sup>, then either ξλ = -λ or M<sup>2n+1</sup> is Einstein. If n = 1, M<sup>3</sup> is locally isometric to the hyperbolic space H<sup>3</sup> (-1).
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.
THREE-DIMENSIONAL LORENTZIAN PARA-KENMOTSU MANIFOLDS AND YAMABE SOLITONS
( Pankaj ),( Sudhakar K. Chaubey ),( Rajendra Prasad ) 호남수학회 2021 호남수학학술지 Vol.43 No.4
The aim of the present work is to study the properties of three-dimensional Lorentzian para-Kenmotsu manifolds equipped with a Yamabe soliton. It is proved that every three-dimensional Lorentzian para-Kenmotsu manifold is Ricci semi-symmetric if and only if it is Einstein. Also, if the metric of a three-dimensional semi-symmetric Lorentzian para-Kenmotsu manifold is a Yamabe soliton, then the soliton is shrinking and the flow vector field is Killing. We also study the properties of threedimensional Ricci symmetric and η-parallel Lorentzian para-Kenmotsu manifolds with Yamabe solitons. Finally, we give a non-trivial example of three-dimensional Lorentzian para-Kenmotsu manifold.
SOME NOTES ON LP-SASAKIAN MANIFOLDS WITH GENERALIZED SYMMETRIC METRIC CONNECTION
( Oğuzhan Bahadir ),( Sudhakar K. Chaubey ) 호남수학회 2020 호남수학학술지 Vol.42 No.3
The present study initially identify the generalized sym- metric connections of type (α;β), which can be regarded as more generalized forms of quarter and semi-symmetric connections. The quarter and semi-symmetric connections are obtained respectively when (α;β) = (1; 0) and (α;β) = (0; 1). Taking that into ac- count, a new generalized symmetric metric connection is attained on Lorentzian para-Sasakian manifolds. In compliance with this connection, some results are obtained through calculation of tensors belonging to Lorentzian para-Sasakian manifold involving curvature tensor, Ricci tensor and Ricci semi-symmetric manifolds. Finally, we consider CR-submanifolds admitting a generalized symmetric metric connection and prove many interesting results.
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.
A NOTE ON ∗-CONFORMAL AND GRADIENT ∗-CONFORMAL η-RICCI SOLITONS IN α-COSYMPLECTIC MANIFOLDS
Abdul Haseeb,Rajendra Prasad,Sudhakar K. Chaubey,Aysel Turgut Vanli 호남수학회 2022 호남수학학술지 Vol.44 No.2
In the present paper we study the properties of α-cosymplectic manifolds endowed with ∗-conformal η-Ricci solitons and gradient ∗-conformal η-Ricci solitons.
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.