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The aim of the present paper is to study some solitons on three dimensional generalized $(\kappa, \mu)$-contact metric manifolds. We study gradient Yamabe solitons on three dimensional generalized $(\kappa, \mu)$-contact metric manifolds. It is proved that if the metric of a three dimensional generalized $(\kappa, \mu)$-contact metric manifold is gradient Einstein soliton then $\mu = \frac{2\kappa}{\kappa - 2}.$ It is shown that if the metric of a three dimensional generalized $(\kappa, \mu)$-contact metric manifold is closed m-quasi Einstein metric then $\kappa = \frac{\lambda}{m + 2}$ and $\mu = 0.$ We also study conformal gradient Ricci solitons on three dimensional generalized $(\kappa, \mu)$-contact metric manifolds.
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참고문헌 (28)
참고문헌 신청
A. Barros / 2012 / Integral formulae on quasi-Einstein manifolds and its applications / Glasgow Math. J 54:213~223
N., Basu / 2015 / conformal Ricci solition in Kenmotsu manifold / Golb. J. Adv. Res. class. Mod. Geom 4:15~21
D. E. Blair / 1976 / Contact Manifolds in Riemannian Geometry / Lecture Notes in Math 509:199~207
D. E. Blair / 1995 / Contact metric manifolds satisying nullity condition / Israel J. Math 91:189~214
D. E. Blair / 2007 / A classification of 3-dimensional contact tensor of a contact metric manifold with Qφ = φQ / Kodai Math. J 13:391~401
N., Basu / 2015 / conformal Ricci solition in Kenmotsu manifold / Golb. J. Adv. Res. class. Mod. Geom 4:15~21
D. E. Blair / 1976 / Contact Manifolds in Riemannian Geometry / Lecture Notes in Math 509:199~207
D. E. Blair / 1995 / Contact metric manifolds satisying nullity condition / Israel J. Math 91:189~214
D. E. Blair / 2007 / A classification of 3-dimensional contact tensor of a contact metric manifold with Qφ = φQ / Kodai Math. J 13:391~401
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