Facebook Instagram Twitter RSS Feed PodBean Back to top on side

$*$-Ricci solitons and gradient almost $*$-Ricci solitons on Kenmotsu manifolds

In: Mathematica Slovaca, vol. 69, no. 6
Venkatesha - Devaraja Mallesha Naik - H. Aruna Kumara
Detaily:
Rok, strany: 2019, 1447 - 1458
Kľúčové slová:
Kenmotsu manifold; *-Ricci soliton; gradient almost *-Ricci soliton; η-Einstein manifold
O článku:
In this paper, we consider $*$-Ricci soliton in the frame-work of Kenmotsu manifolds. First, we prove that if $(M,g)$ is a Kenmotsu manifold and $g$ is a $*$-Ricci soliton, then soliton constant $λ$ is zero. For 3-dimensional case, if $M$ admits a $*$-Ricci soliton, then we show that $M$ is of constant sectional curvature $-1$. Next, we show that if $M$ admits a $*$-Ricci soliton whose potential vector field is collinear with the characteristic vector field $ξ$, then $M$ is Einstein and soliton vector field is equal to $ξ$. Finally, we prove that if $g$ is a gradient almost $*$-Ricci soliton, then either $M$ is Einstein or the potential vector field is collinear with the characteristic vector field on an open set of $M$. We verify our result by constructing examples for both $*$-Ricci soliton and gradient almost $*$-Ricci soliton.
Ako citovať:
ISO 690:
Venkatesha, ., Naik, D., Kumara, H. 2019. $*$-Ricci solitons and gradient almost $*$-Ricci solitons on Kenmotsu manifolds. In Mathematica Slovaca, vol. 69, no.6, pp. 1447-1458. 0139-9918. DOI: https://doi.org/10.1515/ms-2017-0321

APA:
Venkatesha, ., Naik, D., Kumara, H. (2019). $*$-Ricci solitons and gradient almost $*$-Ricci solitons on Kenmotsu manifolds. Mathematica Slovaca, 69(6), 1447-1458. 0139-9918. DOI: https://doi.org/10.1515/ms-2017-0321
O vydaní:
Vydavateľ: Mathematical Institute, Slovak Academy of Sciences, Bratislava
Publikované: 22. 12. 2019