Commun. Korean Math. Soc. 2023; 38(3): 881-892
Online first article April 14, 2023 Printed July 31, 2023
https://doi.org/10.4134/CKMS.c220243
Copyright © The Korean Mathematical Society.
Prakasha Doddabhadrappla Gowda, Devaraja Mallesha Naik, Amruthalakshmi Malleshrao Ravindranatha, Venkatesha Venkatesha
Davangere University; CHRIST (Deemed to be University); Davangere University; Jnana Sahyadri - 577 451
In this paper, we study almost cosymplectic manifolds with nullity distributions admitting Riemann solitons and gradient almost Riemann solitons. First, we consider Riemann soliton on $(\kappa, \mu)$-almost cosymplectic manifold $M$ with $\kappa<0$ and we show that the soliton is expanding with $\lambda = \frac{\kappa}{2n-1}(4n-1)$ and $M$ is locally isometric to the Lie group $G_\rho$. Finally, we prove the non-existence of gradient almost Riemann soliton on a $(\kappa, \mu)$-almost cosymplectic manifold of dimension greater than 3 with $\kappa < 0$.
Keywords: Riemann soliton, almost cosymplectic manifold
MSC numbers: 53C25, 53C25, 53D15
Supported by: The author Amruthalakshmi M. R., is thankful to Department of Science and Technology, Ministry of Science and Technology, Government of India, for providing financial assistance through DST INSPIRE Fellowship (No: DST/INSPIRE Fellowship/[IF 190869]).
2022; 37(1): 213-228
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