On ∗-η-Ricci-Yamabe solitons on LP-Sasakian manifolds
Abstract
In the present paper, geometry of LP-Sasakian manifolds admitting $*-\eta-$Ricci-Yamabe solitons is studied and some characterizations on LP-Sasakian manifolds admitting with $*-\eta-$Ricci-Yamabe solitons are obtained. Finally, the existence of $*-\eta-$Ricci-Yamabe solitons on an LP-Sasakian manifold is proved by constructing a non-trivial example.
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References
\bibitem{ADG} Aqeel, A. A., De, U. C. and Ghosh, G. C., On Lorentzian para-Sasakian manifolds, Kuwait J. Sci. Eng., 31(2)(2004), 1-13.
\bibitem{BLR} Blair, D. E., Contact Manifolds in Riemannian Geometry, Lecture Notes in Math. 509, Springer-Verlag, Berlin, 1976.
\bibitem{CD} Chen, B.Y. and Deshmukh S., Yamabe and quasi-Yamabe solitons on Euclidean submanifolds, Mediterr. J. Math., 15, 194 (2018).
\bibitem{CHEN} Chen, X., Almost quasi-Yamabe solitons on almost cosymplectic manifolds, Int. J. Geom. Methods Mod. Phys. 17(5) (2020) 2050070.
\bibitem{DC} Deshmukh, S. and Chen, B. Y., A note on Yamabe solitons, Balkan Journal of Geometry and Its Applications, 23 (1), (2018), 37-43.
\bibitem{DEC} Dey, C., De, U. C., A note on quasi-Yamabe solitons on contact metric manifolds, J. Geom., 111, 11 (2020).
\bibitem{DED} Dey, D., Almost Kenmotsu metric as Ricci-Yamabe soliton, arXiv:2005.02322 [math.DG].
\bibitem{DR} Dey, S. and Roy, S., $*-\eta-$Ricci Soliton within the framework of Sasakian manifold, Journal of Dynamical Systems and Geomatric Theories, 18 (2020), 163-181.
\bibitem{DGL} Duggal, K. L., Affine conformal vector fields in semi-Riemannian manifolds, Acta Applicandae Mathematicae, 23 (1991), 275-294.
\bibitem{GHOS} Ghosh, A., Ricci soliton and Ricci almost soliton within the framework of Kenmotsu manifold, Carpathian Math. Publ., 11(1) (2019), 59-69.
\bibitem{GC} Guler, S. and Crasmareanu, M., Ricci-Yamabe maps for Riemannian flow and their volume variation and volume entropy, Turk. J. Math., 43 (2019), 2631-2641.
\bibitem{HMD} Hamada, T., Real hypersurfaces of complex space forms in terms of Ricci $*$-tensor, Tokyo J. Math., 25 (2) (2002), 473-483.
\bibitem{HML1} Hamilton, R. S., Lectures on Geometric Flows (Unpublished manuscript, 1989).
\bibitem{HML2} Hamilton, R. S., The Ricci Flow on Surfaces, Mathematics and General Relativity (Santa Cruz, CA, 1986), Contemp. Math., A.M.S., 71 (1988), 237-262.
\bibitem{HC} Haseeb, A. and Chaubey, S. K., Lorentzian para-Sasakian manifolds and $*-$Ricci solitons, Kragujevac Journal of Mathematics, 48(2) (2024), 167-179.
\bibitem{HP1} Haseeb, A. and Prasad, R., $\eta-$Ricci solitons on $\epsilon-$LP-Sasakian manifolds with a quarter-symmetric metric connection, Honam Mathematical J., 41(3) (2019), 539-558.
\bibitem{KMK} Kaimakamis, G. and Panagiotidou, K., $*-$ Ricci solitons of real hypersurfaces in non-flat complex space forms, J. Geom. Phys., 86 (2014), 408-413.
\bibitem{MAT} Matsumoto, K., On Lorentzian paracontact manifolds, Bull. Yamagata Univ. Natur. Sci., 12 (1989), 151-156.
\bibitem{NL} Neill, B. O., Semi-Riemannian Geometry with Applications to Relativity, Academic Press, New York, 1983.
\bibitem{OJH} Ojha, R. H., A note on the $M-$ projective curvature tensor, Indian J. Pure Appl. Math., 8
12 (1975), 1531-1534.
\bibitem{PB}
Prakasha, D. G. and Hadimani, B. S., $\eta-$Ricci solitons on para-Sasakian manifolds, J. Geom., 108 (2017), 383-392.
\bibitem{PV} Prakasha, D. G. and Veeresha, P., Para-Sasakian manifolds and $*-$ Ricci solitons, Afrika Matematika, 30(2018), 989-998.
\bibitem{HP2} Prasad, R. and Haseeb, A., On Lorentzian para-Sasakian manifold with respect to the quarter-symmetric metric connection, Novi Sad J. Math., 62(2) (2016), 103-116.
%\bibitem{SB} Shaikh, A. A. and Baishya, K. K., Some results on $LP-$Sasakian manifolds, Bull. Math. Soc. Sci. Math. Roumanie, %49(97)(2)(2006), 193-205.
\bibitem{Suh} Suh, Y. J. and De, U. C., Yamabe Solitons and Ricci Solitons on almost co-Kahler manifolds, Canad. Math. Bull. Vol. 62 (2019), 653-661.
\bibitem{TACH} Tachibana, S., On almost-analytic vectors in almost-Kahlerian manifolds, Tohoku Math. J. (2), 11 (1959), no 2, 247-265.
\bibitem{VENK} Venkatesha, Naik, D. M. and Kumara, H. A., $*-$ Ricci solitons and gradient almost $*-$Ricci
solitons on Kenmotsu manifolds, Mathematica Slovaca, 69(2019), 1447-1458.
\bibitem{YANO} Yano, K., Integral Formulas in Riemannian Geometry, Marcel Dekker, New York (1970).
\bibitem{YDA} Yildiz A., De, U. C. and Ata, E., On a type of Lorentzian para-Sasakian manifolds, Math. Reports, 16(66)(1), 61-67.
\bibitem{YLDS} Yoldas, H. I., Meric, S. E. and Yasar, E., Some characterizations of $\alpha-$cosymplectic manifolds admitting Yamabe solitons, Palestine Journal of Mathematics, 10(1)(2021), 234-241.
\bibitem{LI} Zhang, P., Li, Y., Roy, S. and Dey, S., Geometry of $\alpha-$cosymplectic metric as $*-$Conformal $\eta-$Ricci-Yamabe solitons admitting quarter-symmetric metric connection, Symmetry, 13(11) (2021) : 2189.\\
\bibitem{BLR} Blair, D. E., Contact Manifolds in Riemannian Geometry, Lecture Notes in Math. 509, Springer-Verlag, Berlin, 1976.
\bibitem{CD} Chen, B.Y. and Deshmukh S., Yamabe and quasi-Yamabe solitons on Euclidean submanifolds, Mediterr. J. Math., 15, 194 (2018).
\bibitem{CHEN} Chen, X., Almost quasi-Yamabe solitons on almost cosymplectic manifolds, Int. J. Geom. Methods Mod. Phys. 17(5) (2020) 2050070.
\bibitem{DC} Deshmukh, S. and Chen, B. Y., A note on Yamabe solitons, Balkan Journal of Geometry and Its Applications, 23 (1), (2018), 37-43.
\bibitem{DEC} Dey, C., De, U. C., A note on quasi-Yamabe solitons on contact metric manifolds, J. Geom., 111, 11 (2020).
\bibitem{DED} Dey, D., Almost Kenmotsu metric as Ricci-Yamabe soliton, arXiv:2005.02322 [math.DG].
\bibitem{DR} Dey, S. and Roy, S., $*-\eta-$Ricci Soliton within the framework of Sasakian manifold, Journal of Dynamical Systems and Geomatric Theories, 18 (2020), 163-181.
\bibitem{DGL} Duggal, K. L., Affine conformal vector fields in semi-Riemannian manifolds, Acta Applicandae Mathematicae, 23 (1991), 275-294.
\bibitem{GHOS} Ghosh, A., Ricci soliton and Ricci almost soliton within the framework of Kenmotsu manifold, Carpathian Math. Publ., 11(1) (2019), 59-69.
\bibitem{GC} Guler, S. and Crasmareanu, M., Ricci-Yamabe maps for Riemannian flow and their volume variation and volume entropy, Turk. J. Math., 43 (2019), 2631-2641.
\bibitem{HMD} Hamada, T., Real hypersurfaces of complex space forms in terms of Ricci $*$-tensor, Tokyo J. Math., 25 (2) (2002), 473-483.
\bibitem{HML1} Hamilton, R. S., Lectures on Geometric Flows (Unpublished manuscript, 1989).
\bibitem{HML2} Hamilton, R. S., The Ricci Flow on Surfaces, Mathematics and General Relativity (Santa Cruz, CA, 1986), Contemp. Math., A.M.S., 71 (1988), 237-262.
\bibitem{HC} Haseeb, A. and Chaubey, S. K., Lorentzian para-Sasakian manifolds and $*-$Ricci solitons, Kragujevac Journal of Mathematics, 48(2) (2024), 167-179.
\bibitem{HP1} Haseeb, A. and Prasad, R., $\eta-$Ricci solitons on $\epsilon-$LP-Sasakian manifolds with a quarter-symmetric metric connection, Honam Mathematical J., 41(3) (2019), 539-558.
\bibitem{KMK} Kaimakamis, G. and Panagiotidou, K., $*-$ Ricci solitons of real hypersurfaces in non-flat complex space forms, J. Geom. Phys., 86 (2014), 408-413.
\bibitem{MAT} Matsumoto, K., On Lorentzian paracontact manifolds, Bull. Yamagata Univ. Natur. Sci., 12 (1989), 151-156.
\bibitem{NL} Neill, B. O., Semi-Riemannian Geometry with Applications to Relativity, Academic Press, New York, 1983.
\bibitem{OJH} Ojha, R. H., A note on the $M-$ projective curvature tensor, Indian J. Pure Appl. Math., 8
12 (1975), 1531-1534.
\bibitem{PB}
Prakasha, D. G. and Hadimani, B. S., $\eta-$Ricci solitons on para-Sasakian manifolds, J. Geom., 108 (2017), 383-392.
\bibitem{PV} Prakasha, D. G. and Veeresha, P., Para-Sasakian manifolds and $*-$ Ricci solitons, Afrika Matematika, 30(2018), 989-998.
\bibitem{HP2} Prasad, R. and Haseeb, A., On Lorentzian para-Sasakian manifold with respect to the quarter-symmetric metric connection, Novi Sad J. Math., 62(2) (2016), 103-116.
%\bibitem{SB} Shaikh, A. A. and Baishya, K. K., Some results on $LP-$Sasakian manifolds, Bull. Math. Soc. Sci. Math. Roumanie, %49(97)(2)(2006), 193-205.
\bibitem{Suh} Suh, Y. J. and De, U. C., Yamabe Solitons and Ricci Solitons on almost co-Kahler manifolds, Canad. Math. Bull. Vol. 62 (2019), 653-661.
\bibitem{TACH} Tachibana, S., On almost-analytic vectors in almost-Kahlerian manifolds, Tohoku Math. J. (2), 11 (1959), no 2, 247-265.
\bibitem{VENK} Venkatesha, Naik, D. M. and Kumara, H. A., $*-$ Ricci solitons and gradient almost $*-$Ricci
solitons on Kenmotsu manifolds, Mathematica Slovaca, 69(2019), 1447-1458.
\bibitem{YANO} Yano, K., Integral Formulas in Riemannian Geometry, Marcel Dekker, New York (1970).
\bibitem{YDA} Yildiz A., De, U. C. and Ata, E., On a type of Lorentzian para-Sasakian manifolds, Math. Reports, 16(66)(1), 61-67.
\bibitem{YLDS} Yoldas, H. I., Meric, S. E. and Yasar, E., Some characterizations of $\alpha-$cosymplectic manifolds admitting Yamabe solitons, Palestine Journal of Mathematics, 10(1)(2021), 234-241.
\bibitem{LI} Zhang, P., Li, Y., Roy, S. and Dey, S., Geometry of $\alpha-$cosymplectic metric as $*-$Conformal $\eta-$Ricci-Yamabe solitons admitting quarter-symmetric metric connection, Symmetry, 13(11) (2021) : 2189.\\
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2025-09-01
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