GEOMETRY OF $\upeta$-RICCI YAMABE SOLITON ON NEARLY SASAKIAN MANIFOLD
Abstract
The present paper is devoted to study $\upeta$-Ricci-Yamabe soliton on nearly-Sasakian manifolds. We examine Ricci-semisymmetricity and Einstein- semisymmetric on nearly-sasakian manifold to obtain condition for shrinking or steady or expanding. Further, we analyze the 3-dimensional nearly-Sasakian manifolds admitting $\upeta$-Ricci-Yamabe soliton satisfying certain geometric conditions.
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References
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P. Siva Kota Reddy, Ricci-Yamabe Solitons on Submanifolds of Some Indefinite Almost Contact Manifolds, \emph{Adv. Math., Sci. J.}, \textbf{9}(11) (2020), 10067--10080.
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P. Siva Kota Reddy, Ricci Solitons on $(LCS)$-Manifolds under $D$-Homothetic Deformation, \emph{ Ital. J. Pure Appl. Math.}, \textbf{46} (2021), 672-683.
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\bibitem{som3} G. Somashekhara, P. Siva Kota Reddy, N. Pavani and G. J. Manjula, $\upeta$-Ricci-Yamabe Solitons on Submanifolds of some Indefinite almost Contact Manifolds, \emph{J. Math. Comput. Sci.}, \textbf{11}(3) (2021), 3775--3791.
\bibitem{som4} G. Somashekhara, S. Girish Babu and P. Siva Kota Reddy, Conformal Ricci Soliton in an Indefinite Trans-Sasakian manifold, {Vladikavkaz Math. J}, \textbf{23}(3) (2021), 43--49.
\bibitem{som5} G. Somashekhara, S. Girish Babu and P. Siva Kota Reddy, Ricci Solitons and Generalized Weak Symmetries under $D$-Homothetically Deformed $LP$-Sasakian Manifolds, \emph{ Ital. J. Pure Appl. Math.}, \textbf{46} (2021), 684--695.
\bibitem{som6} G. Somashekhara, S. Girish Babu and P. Siva Kota Reddy, Conformal $\upeta$-Ricci Solitons in Lorentzian Para-Sasakian Manifold Admitting Semi-Symmetric Metric Connection, \emph{ Ital. J. Pure Appl. Math.}, \textbf{46} (2021), 1008--1019.
\bibitem{som11} G. Somashekhara, S. Girish Babu and P. Siva Kota Reddy, $\upeta$-Ricci soliton in an indefinite trans-Sasakian manifold admitting semi-symmetric metric connection, \emph{Bol. Soc. Parana. Mat. (3)}, \textbf{41} (2023), 1--9.
\bibitem{y3} M. D. Siddiqi and M. A. Akyol, $\upeta$-Ricci-Yamabe Soliton on Riemannian Submersions from Riemannian manifolds, arxiv preprint arxiv:2004.14124, (2020).
P. Siva Kota Reddy, Ricci-Yamabe Solitons on Submanifolds of Some Indefinite Almost Contact Manifolds, \emph{Adv. Math., Sci. J.}, \textbf{9}(11) (2020), 10067--10080.
\bibitem{ang1} P. G. Angadi, G. S. Shivaprasanna, G. Somashekhara and
P. Siva Kota Reddy, Ricci Solitons on $(LCS)$-Manifolds under $D$-Homothetic Deformation, \emph{ Ital. J. Pure Appl. Math.}, \textbf{46} (2021), 672-683.
\bibitem{y1} J. T. Cho, M. Kimura, Ricci solitons and Real hypersurfaces in a complex
space form, \emph{Tohoku Math. J.}, 61(2) (2009), 205-212.
\bibitem{y2} R. S. Hamilton, The Ricci flow on surfaces, \emph{Contemp. Math.}, 71 (1988), 237-261.
\bibitem{som3} G. Somashekhara, P. Siva Kota Reddy, N. Pavani and G. J. Manjula, $\upeta$-Ricci-Yamabe Solitons on Submanifolds of some Indefinite almost Contact Manifolds, \emph{J. Math. Comput. Sci.}, \textbf{11}(3) (2021), 3775--3791.
\bibitem{som4} G. Somashekhara, S. Girish Babu and P. Siva Kota Reddy, Conformal Ricci Soliton in an Indefinite Trans-Sasakian manifold, {Vladikavkaz Math. J}, \textbf{23}(3) (2021), 43--49.
\bibitem{som5} G. Somashekhara, S. Girish Babu and P. Siva Kota Reddy, Ricci Solitons and Generalized Weak Symmetries under $D$-Homothetically Deformed $LP$-Sasakian Manifolds, \emph{ Ital. J. Pure Appl. Math.}, \textbf{46} (2021), 684--695.
\bibitem{som6} G. Somashekhara, S. Girish Babu and P. Siva Kota Reddy, Conformal $\upeta$-Ricci Solitons in Lorentzian Para-Sasakian Manifold Admitting Semi-Symmetric Metric Connection, \emph{ Ital. J. Pure Appl. Math.}, \textbf{46} (2021), 1008--1019.
\bibitem{som11} G. Somashekhara, S. Girish Babu and P. Siva Kota Reddy, $\upeta$-Ricci soliton in an indefinite trans-Sasakian manifold admitting semi-symmetric metric connection, \emph{Bol. Soc. Parana. Mat. (3)}, \textbf{41} (2023), 1--9.
\bibitem{y3} M. D. Siddiqi and M. A. Akyol, $\upeta$-Ricci-Yamabe Soliton on Riemannian Submersions from Riemannian manifolds, arxiv preprint arxiv:2004.14124, (2020).
Published
2025-01-21
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