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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.
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.