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The object of the offering exposition is to study almost Ricci soliton and gradient almost Ricci soliton in 3-dimensional para-Sasakian manifolds. At first, it is shown that if $(g, V,\lambda)$ be an almost Ricci soliton on a 3-dimensional para-Sasakian manifold $M$, then it reduces to a Ricci soliton and the soliton is expanding for $\lambda$=-2. Besides these, in this section, we prove that if $V$ is pointwise collinear with $\xi$, then $V$ is a constant multiple of $\xi$ and the manifold is of constant sectional curvature $-1$. Moreover, it is proved that if a 3-dimensional para-Sasakian manifold admits gradient almost Ricci soliton under certain conditions then either the manifold is of constant sectional curvature $-1$ or it reduces to a gradient Ricci soliton. Finally, we consider an example to justify some results of our paper.
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참고문헌 (20)
참고문헌 신청
Barros, A. / Compact almost Ricci solitons with constant scalar curvature are gradient / Monatsh. Math
Barros, A. / 2012 / Some characterizations for Compact almost Ricci solitons / Proc. Amer. Math. Soc 140:1033~1040
Blaga, A.M. / 2019 / Some Geometrical Aspects of Einstein, Ricci and Yamabe solitons / J. Geom. symmetry Phys. 52:17~26
Blaga, A.M. / 2015 / η-Ricci solitons on para-Kenmotsu manifolds / Balkan J. Geom. Appl 20:1~13
Cappelletti-Montano, B / 2012 / Nullity conditions in paracontact geometry / Differ. Geom. Appl 30:665~693
Barros, A. / 2012 / Some characterizations for Compact almost Ricci solitons / Proc. Amer. Math. Soc 140:1033~1040
Blaga, A.M. / 2019 / Some Geometrical Aspects of Einstein, Ricci and Yamabe solitons / J. Geom. symmetry Phys. 52:17~26
Blaga, A.M. / 2015 / η-Ricci solitons on para-Kenmotsu manifolds / Balkan J. Geom. Appl 20:1~13
Cappelletti-Montano, B / 2012 / Nullity conditions in paracontact geometry / Differ. Geom. Appl 30:665~693
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