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RICCI SOLITONS ON RICCI PSEUDOSYMMETRIC (LCS)<sub>n</sub>-MANIFOLDS
( Shyamal Kumar Hui ),( Richard S. Lemence ),( Debabrata Chakraborty ) 호남수학회 2018 호남수학학술지 Vol.40 No.2
The object of the present paper is to study some types of Ricci pseudosymmetric (LCS)<sub>n</sub>-manifolds whose metric is Ricci soliton. We found the conditions when Ricci soliton on concircu-lar Ricci pseudosymmetric, projective Ricci pseudosymmetric, W<sub>3</sub>- Ricci pseudosymmetric, conharmonic Ricci pseudosymmetric, con-formal Ricci pseudosymmetric (LCS)<sub>n</sub>-manifolds to be shrinking, steady and expanding. We also construct an example of concircu-lar Ricci pseudosymmetric (LCS)<sub>3</sub>-manifold whose metric is Ricci soliton.
On φ-pseudo Symmetries of (LCS)<sub>n</sub>-Manifolds
Hui, Shyamal Kumar Department of Mathematics 2013 Kyungpook mathematical journal Vol.53 No.2
The present paper deals with a study of ${\phi}$-pseudo symmetric and ${\phi}$-pseudo Ricci symmetric $(LCS)_n$-manifolds. It is shown that every ${\phi}$-pseudo symmetric $(LCS)_n$-manifold and ${\phi}$-pseudo Ricci symmetric $(LCS)_n$-manifold are ${\eta}$-Einstein manifold.
ON GENERALIZED WEAKLY SEMI-CONFORMALLY SYMMETRIC MANIFOLDS
Hui, Shyamal Kumar,Patra, Akshoy,Patra, Ananta Korean Mathematical Society 2021 대한수학회논문집 Vol.36 No.4
In this paper we introduce generalized weakly semi-conformally symmetric manifold, a generalization of weakly symmetric manifold. We study some basic properties and obtain the forms of the scalar curvature of such manifold. In the last section an example is given to ensure the existence of such manifold.
On Generalized 𝜙-recurrent Kenmotsu Manifolds with respect to Quarter-symmetric Metric Connection
Hui, Shyamal Kumar,Lemence, Richard Santiago Department of Mathematics 2018 Kyungpook mathematical journal Vol.58 No.2
A Kenmotsu manifold $M^n({\phi},\;{\xi},\;{\eta},\;g)$, (n = 2m + 1 > 3) is called a generalized ${\phi}-recurrent$ if its curvature tensor R satisfies $${\phi}^2(({\nabla}_wR)(X,Y)Z)=A(W)R(X,Y)Z+B(W)G(X,Y)Z$$ for all $X,\;Y,\;Z,\;W{\in}{\chi}(M)$, where ${\nabla}$ denotes the operator of covariant differentiation with respect to the metric g, i.e. ${\nabla}$ is the Riemannian connection, A, B are non-vanishing 1-forms and G is given by G(X, Y)Z = g(Y, Z)X - g(X, Z)Y. In particular, if A = 0 = B then the manifold is called a ${\phi}-symmetric$. Now, a Kenmotsu manifold $M^n({\phi},\;{\xi},\;{\eta},\;g)$, (n = 2m + 1 > 3) is said to be generalized ${\phi}-Ricci$ recurrent if it satisfies $${\phi}^2(({\nabla}_wQ)(Y))=A(X)QY+B(X)Y$$ for any vector field $X,\;Y{\in}{\chi}(M)$, where Q is the Ricci operator, i.e., g(QX, Y) = S(X, Y) for all X, Y. In this paper, we study generalized ${\phi}-recurrent$ and generalized ${\phi}-Ricci$ recurrent Kenmotsu manifolds with respect to quarter-symmetric metric connection and obtain a necessary and sufficient condition of a generalized ${\phi}-recurrent$ Kenmotsu manifold with respect to quarter symmetric metric connection to be generalized Ricci recurrent Kenmotsu manifold with respect to quarter symmetric metric connection.
CHARACTERIZATION OF WARPED PRODUCT SUBMANIFOLDS OF LORENTZIAN CONCIRCULAR STRUCTURE MANIFOLDS
Hui, Shyamal Kumar,Pal, Tanumoy,Piscoran, Laurian Ioan Korean Mathematical Society 2019 대한수학회논문집 Vol.34 No.4
Recently Hui et al. ([8,9]) studied contact CR-warped product submanifolds and also warped product pseudo-slant submanifolds of a $(LCS)_n$-manifold $\bar{M}$. The characterization for both these classes of warped product submanifolds have been studied here. It is also shown that there do not exists any proper warped product bi-slant submanifold of a $(LCS)_n$-manifold. Although the existence of a bi-slant submanifold of $(LCS)_n$-manifold is ensured by an example.
RICCI SOLITONS ON RICCI PSEUDOSYMMETRIC (LCS)<sub>n</sub>-MANIFOLDS
Hui, Shyamal Kumar,Lemence, Richard S.,Chakraborty, Debabrata The Honam Mathematical Society 2018 호남수학학술지 Vol.40 No.2
The object of the present paper is to study some types of Ricci pseudosymmetric $(LCS)_n$-manifolds whose metric is Ricci soliton. We found the conditions when Ricci soliton on concircular Ricci pseudosymmetric, projective Ricci pseudosymmetric, $W_3$-Ricci pseudosymmetric, conharmonic Ricci pseudosymmetric, conformal Ricci pseudosymmetric $(LCS)_n$-manifolds to be shrinking, steady and expanding. We also construct an example of concircular Ricci pseudosymmetric $(LCS)_3$-manifold whose metric is Ricci soliton.
YAMABE SOLITONS ON KENMOTSU MANIFOLDS
Hui, Shyamal Kumar,Mandal, Yadab Chandra Korean Mathematical Society 2019 대한수학회논문집 Vol.34 No.1
The present paper deals with a study of infinitesimal CL-transformations on Kenmotsu manifolds, whose metric is Yamabe soliton and obtained sufficient conditions for such solitons to be expanding, steady and shrinking. Among others, we find a necessary and sufficient condition of a Yamabe soliton on Kenmotsu manifold with respect to CL-connection to be Yamabe soliton on Kenmotsu manifold with respect to Levi-Civita connection. We found the necessary and sufficient condition for the Yamabe soliton structure to be invariant under Schouten-Van Kampen connection. Finally, we constructed an example of steady Yamabe soliton on 3-dimensional Kenmotsu manifolds with respect to Schouten-Van Kampen connection.
RICCI SOLITONS ON RICCI PSEUDOSYMMETRIC (LCS)n-MANIFOLDS
SHYAMAL KUMAR HUI,Richard S. Lemence,Debabrata Chakraborty 호남수학회 2018 호남수학학술지 Vol.40 No.2
The object of the present paper is to study some typesof Ricci pseudosymmetric (LCS)n-manifolds whose metric is Riccisoliton. We found the conditions when Ricci soliton on concircularRicci pseudosymmetric, projective Ricci pseudosymmetric, W3-Ricci pseudosymmetric, conharmonic Ricci pseudosymmetric, conformalRicci pseudosymmetric (LCS)n-manifolds to be shrinking,steady and expanding. We also construct an example of concircularRicci pseudosymmetric (LCS)3-manifold whose metric is Riccisoliton.
A NOTE ON (k, μ)′ -ALMOST KENMOTSU MANIFOLDS
( Sunil Kumar Yadav ),( Yadab Chandra Mandal ),( Shyamal Kumar Hui ) 호남수학회 2021 호남수학학술지 Vol.43 No.4
The present paper deals with the study of generalized quasiconformal curvature tensor inside the setting of (k, μ)′ -almost Kenmotsu manifold with respect to η-Ricci soliton. Certain consequences of these curvature tensor on such manifold are likewise displayed. Finally, we illustrate some examples based on this study.
SECOND ORDER PARALLEL TENSORS AND RICCI SOLITONS ON (LCS)<sub>n</sub>-MANIFOLDS
Chandra, Soumen,Hui, Shyamal Kumar,Shaikh, Absos Ali Korean Mathematical Society 2015 대한수학회논문집 Vol.30 No.2
The object of the present paper is to study the second order parallel symmetric tensors and Ricci solitons on $(LCS)_n$-manifolds. We found the conditions of Ricci soliton on $(LCS)_n$-manifolds to be shrinking, steady and expanding respectively.