Warped product spaces with Ricci conditions

Abstract

In this paper, we study the Ricci soliton in the Riemannian products M = R n × B and warped products M = R × f B of the Euclidean space and Riemannian manifolds, and the gradient Ricci soliton in the warped products M = S 1 × f B of 1-dimensional circle and Riemannian manifolds. Moreover, we introduce the concept of the generalized Ricci soliton and we suggest the method of construction of the Riemannian manifold (M, g) with a Ricci soliton g .Finally, we also study the Lorentzian warped products with the Ricci soliton.

On Warped Product Gradient Ricci-Harmonic Soliton

“…In recent works on soliton, the notion of warped product introduced in ([3]), has become an important tool in the construction of manifolds with certain geometric properties [1,5,12].…”

On sequential warped product manifolds admitting gradient Ricci-harmonic solitons

“…For some studies about sequential warped Since the study of solitons and warped product manifolds together is interesting in terms of their role in general relativity, it has been studied by many authors in the recent years. For more information on solitons with the structure of warped product manifolds and their some generalizations see also [27][28][29][30][31][32][33][34] and [35]. By a motivation from the above studies, in the present paper, we consider gradient Ricci-harmonic solitons on sequential warped products.…”

Gradient Yamabe Solitons on Multiply Warped Product Manifolds

“…In [16], Tokura, Adriano, Pina and Barboza studied gradient Yamabe soliton on warped product manifolds with limited warping function, and for the compact base. For other developments about Ricci solitons and gradient Ricci soliton; [3], [5], [8], [9], [10], [13], [17]. Motivated by the above studies, in the present paper, we consider gradient Yamabe solitons on multiply warped product manifolds.…”