Browsing by Subject "Warped product manifolds"
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Item Open Access Concircular curvature on warped product manifolds and applications(Springer, 2020-09) De, U. C.; Shenawy, S.; Ünal, BülentThis study aims mainly at investigating the effects of concircular flatness and concircular symmetry of a warped product manifold on its fiber and base manifolds. Concircularly flat and concircularly symmetric warped product manifolds are investigated. The divergence-free concircular curvature tensor on warped product manifolds is considered. Finally, we apply some of these results to generalized Robertson–Walker and standard static space-times.Item Open Access The existence of gradient Yamabe solitons on spacetimes(Springer, 2022-10) Güler, S.; Ünal, BülentThe main aim of the present article is to study generalized quasi-Yamabe gradient solitons on warped product manifolds. First, we obtain some necessary and sufficient conditions for the existence of generalized quasi-Yamabe gradient solitons equipped on a warped product structure. Then we study some important applications in the Lorentzian and the neutral settings for the particular class, called as gradient Yamabe soliton. More explicitly, we prove the existence of the non-trivial gradient Yamabe soliton on generalized Robertson–Walker spacetimes, standard static spacetimes, Walker manifolds and pp-wave spacetimes. © 2022, The Author(s), under exclusive licence to Springer Nature Switzerland AG.Item Open Access Ricci solitons on singly warped product manifolds and applications(Elsevier BV * North-Holland, 2021-08) De, U. C.; Mantica, C. A.; Shenawy, S.; Ünal, BülentThe purpose of this article is to study implications of a Ricci soliton warped product manifold to its base and fiber manifolds. First, it is proved that if a warped product manifold is Ricci soliton then its factors are Ricci soliton. Then we study Ricci soliton on warped product manifolds admitting either a conformal vector field or a concurrent vector field. Finally, we study Ricci soliton on some warped product space-times.