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Let $(M^{2n+1},\phi,\xi,\eta,g)$ be a $(k,\mu)'$-almost Kenmotsu manifold with $k<-1$ which admits a gradient Ricci almost soliton $(g,f,\lambda)$, where $\lambda$ is the soliton function and $f$ is the potential function. In this paper, it is proved that $\lambda$ is a constant and this implies that $M^{2n+1}$ is locally isometric to a rigid gradient Ricci soliton $\mathbb{H}^{n+1}(-4)\times\mathbb{R}^n$, and the soliton is expanding with $\lambda=-4n$. Moreover, if a three dimensional Kenmotsu manifold admits a gradient Ricci almost soliton, then either it is of constant sectional curvature $-1$ or the potential vector field is pointwise colinear with the Reeb vector field.
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참고문헌 (26)
참고문헌 신청
A. Barros / 2014 / Compact almost Ricci solitons with constant scalar curvature are gradient / Monatsh. Math 174(1):29~39
D. E. Blair / 2010 / Riemannian geometry of contact and symplectic manifolds, Progress in Mathematics, Volume 203 / Birkh¨auser
C. P. Boyer / 2001 / Einstein manifolds and contact geometry / Proc. Amer. Math. Soc 129(8):2419~2430
C. Calin / 2010 / From the Eisenhart problem to Ricci solitons in fKenmotsu manifolds / Bull. Malays. Math. Sci. Soc 33(3):361~368
J. T. Cho / 2013 / Almost contact 3-manifolds and Ricci solitons / Int. J. Geom. Methods Mod. Phys 10(1):7
D. E. Blair / 2010 / Riemannian geometry of contact and symplectic manifolds, Progress in Mathematics, Volume 203 / Birkh¨auser
C. P. Boyer / 2001 / Einstein manifolds and contact geometry / Proc. Amer. Math. Soc 129(8):2419~2430
C. Calin / 2010 / From the Eisenhart problem to Ricci solitons in fKenmotsu manifolds / Bull. Malays. Math. Sci. Soc 33(3):361~368
J. T. Cho / 2013 / Almost contact 3-manifolds and Ricci solitons / Int. J. Geom. Methods Mod. Phys 10(1):7
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