In this paper, we examine 3-dimensional quasi-Sasakian manifold admitting conformal Ricci soliton. We give some theorems for $W_{0}^{*}$ flat, $\xi-W_{0}^{*}$ flat and $\phi-W_{0}^{*}$ semisymmetric 3-dimensional quasi-Sasakian manifold admitting conformal Ricci soliton. Also we study conformal Ricci soliton on a 3-dimensional quasi-Sasakian manifold satisfying the conditions $W_{0}^{*}(\xi,X).S=0$ and $R(\xi,X).W_{0}^{*}=0$.
Blair, D.E., The theory of quasi-Sasakian structures, J. Diff Geo., 1(1967), 331–345.
Calin, C., Crasmareanu, M., From the Eisenhart problem to Ricci solitons in f−Kenmotsu manifolds, Bull. Malays. Math. Sci. Soc., 33(3)(2010), 361–368.
Cho, J.T., Kimura M., Ricci solitons and real hypersurfaces in a complex space form, Tohoku Math. J., 61(2)(2009), 205–212.
De, U.C., Majhi P., φ−semisymmetric generalized Sasakian space-forms, Arab J. Math. Sci., 21(2)(2015), 170–178.
De, U.C., Mondal, A.K., 3-dimensional quasi-Sasakian manifolds and Ricci solitons, SUT J. Math., 48(1)(2012), 71–81.
De, U.C., Sarkar, A., On three-dimensional quasi-Sasakian manifolds, SUT J. Math., 45(1) 2009), 59–71.
De, U.C., Yildiz, A., Turan, M., Acet, B. E., 3-dimensional quasi-Sasakian manifolds with semi-symmetric non-metric connection, Hacettepe J. Math. Stat., 41(1)(2012), 127–137.
De, U.C., De, K., Khan, M.N.I., Almost co-K¨ahler manifolds and quasi-Einstein solitons, Chaos, Solitons and Fractals, 167(2023).
Fischer, A.E., An introduction to conformal Ricci flow class, Quantum Grav., 21(3)(2004), 171–218.
Gautam, U.K., Haseeb, A., Prasad R., Some results on projective curvature tensor in Sasakian manifolds, Commun. Korean Math. Soc., 34(3)(2019), 881–896.
Ghosh, S., η−Ricci solitons on quasi-Sasakian manifolds, An. Univ. Vest Timi¸s. Ser. Mat.-Inform., 56(1)(2018), 73–85.
Gonzalez, J.C., Chinea, D., Quasi-Sasakian homogeneous structures on the generalized Heisenberg group H(p, 1), Proc. Amer. Math. Soc., 105(1)(1989), 173–184.
Haseeb, A., Prasad, R., η−Ricci solitons on ε−LP-Sasakian manifolds with a quartersymmetric metric connection, Honam Math. J., 41(3)(2019), 539–558.
Haseeb, A., Bilal, M., Chaubey, S.K., Khan, M.N.I., Geometry of indefinite Kenmotsu manifolds as ∗η-Ricci-Yamabe solitons, Axioms, 11(9)(2022), 461.
Blair, D.E., The theory of quasi-Sasakian structures, J. Diff Geo., 1(1967), 331–345.
Calin, C., Crasmareanu, M., From the Eisenhart problem to Ricci solitons in f−Kenmotsu manifolds, Bull. Malays. Math. Sci. Soc., 33(3)(2010), 361–368.
Cho, J.T., Kimura M., Ricci solitons and real hypersurfaces in a complex space form, Tohoku Math. J., 61(2)(2009), 205–212.
De, U.C., Majhi P., φ−semisymmetric generalized Sasakian space-forms, Arab J. Math. Sci., 21(2)(2015), 170–178.
De, U.C., Mondal, A.K., 3-dimensional quasi-Sasakian manifolds and Ricci solitons, SUT J. Math., 48(1)(2012), 71–81.
De, U.C., Sarkar, A., On three-dimensional quasi-Sasakian manifolds, SUT J. Math., 45(1) 2009), 59–71.
De, U.C., Yildiz, A., Turan, M., Acet, B. E., 3-dimensional quasi-Sasakian manifolds with semi-symmetric non-metric connection, Hacettepe J. Math. Stat., 41(1)(2012), 127–137.
De, U.C., De, K., Khan, M.N.I., Almost co-K¨ahler manifolds and quasi-Einstein solitons, Chaos, Solitons and Fractals, 167(2023).
Fischer, A.E., An introduction to conformal Ricci flow class, Quantum Grav., 21(3)(2004), 171–218.
Gautam, U.K., Haseeb, A., Prasad R., Some results on projective curvature tensor in Sasakian manifolds, Commun. Korean Math. Soc., 34(3)(2019), 881–896.
Ghosh, S., η−Ricci solitons on quasi-Sasakian manifolds, An. Univ. Vest Timi¸s. Ser. Mat.-Inform., 56(1)(2018), 73–85.
Gonzalez, J.C., Chinea, D., Quasi-Sasakian homogeneous structures on the generalized Heisenberg group H(p, 1), Proc. Amer. Math. Soc., 105(1)(1989), 173–184.
Haseeb, A., Prasad, R., η−Ricci solitons on ε−LP-Sasakian manifolds with a quartersymmetric metric connection, Honam Math. J., 41(3)(2019), 539–558.
Haseeb, A., Bilal, M., Chaubey, S.K., Khan, M.N.I., Geometry of indefinite Kenmotsu manifolds as ∗η-Ricci-Yamabe solitons, Axioms, 11(9)(2022), 461.
Akgün, M. A., & Acet, B. E. (2023). Some Curvature Conditions on 3-Dimensional Quasi-Sasakian Manifolds Admitting Conformal Ricci Soliton. Turkish Journal of Mathematics and Computer Science, 15(2), 375-381. https://doi.org/10.47000/tjmcs.1082849
AMA
Akgün MA, Acet BE. Some Curvature Conditions on 3-Dimensional Quasi-Sasakian Manifolds Admitting Conformal Ricci Soliton. TJMCS. December 2023;15(2):375-381. doi:10.47000/tjmcs.1082849
Chicago
Akgün, Müslüm Aykut, and Bilal Eftal Acet. “Some Curvature Conditions on 3-Dimensional Quasi-Sasakian Manifolds Admitting Conformal Ricci Soliton”. Turkish Journal of Mathematics and Computer Science 15, no. 2 (December 2023): 375-81. https://doi.org/10.47000/tjmcs.1082849.
EndNote
Akgün MA, Acet BE (December 1, 2023) Some Curvature Conditions on 3-Dimensional Quasi-Sasakian Manifolds Admitting Conformal Ricci Soliton. Turkish Journal of Mathematics and Computer Science 15 2 375–381.
IEEE
M. A. Akgün and B. E. Acet, “Some Curvature Conditions on 3-Dimensional Quasi-Sasakian Manifolds Admitting Conformal Ricci Soliton”, TJMCS, vol. 15, no. 2, pp. 375–381, 2023, doi: 10.47000/tjmcs.1082849.
ISNAD
Akgün, Müslüm Aykut - Acet, Bilal Eftal. “Some Curvature Conditions on 3-Dimensional Quasi-Sasakian Manifolds Admitting Conformal Ricci Soliton”. Turkish Journal of Mathematics and Computer Science 15/2 (December 2023), 375-381. https://doi.org/10.47000/tjmcs.1082849.
JAMA
Akgün MA, Acet BE. Some Curvature Conditions on 3-Dimensional Quasi-Sasakian Manifolds Admitting Conformal Ricci Soliton. TJMCS. 2023;15:375–381.
MLA
Akgün, Müslüm Aykut and Bilal Eftal Acet. “Some Curvature Conditions on 3-Dimensional Quasi-Sasakian Manifolds Admitting Conformal Ricci Soliton”. Turkish Journal of Mathematics and Computer Science, vol. 15, no. 2, 2023, pp. 375-81, doi:10.47000/tjmcs.1082849.
Vancouver
Akgün MA, Acet BE. Some Curvature Conditions on 3-Dimensional Quasi-Sasakian Manifolds Admitting Conformal Ricci Soliton. TJMCS. 2023;15(2):375-81.