Recently, the author established a general inequality for doubly warped products in arbitrary Riemannian manifolds [14]. In the present paper, we obtain a similar inequality for doubly warped products isometrically immersed in S-space forms. As applications, we derive certain obstructions to the existence of minimal isometric immersions of doubly warped product integral submanifolds in S-space ...

Information geometry is an important tool to study statistical models. There are some examples in models which regarded as warped products. In this paper, we information of We consider the case where product and its fiber space equipped with dually flat connections and, particular a cone, characterize on base $$\mathbb {R}_{>0}$$ . The resulting turn out be $$\alpha $$ -connections = \pm {1}$$

The linear stability of warped product Einstein metrics as fixed points the Ricci flow is investigated. We generalise results Gibbons, Hartnoll and Pope show that in sufficiently low dimensions, all are unstable. By exploiting relationship between metrics, quasi-Einstein solitons, we introduce a new destabilising perturbation (the variation) certain infinite families will be unstable high dimen...

In this paper we prove that there do not exist warped product GCR-lightlike submanifolds in the form M = N⊥ ×λ NT such that N⊥ is an anti-invariant submanifold tangent to V and NT an invariant submanifold of M̄ , other than GCR-lightlike product in an indefinite cosymplectic manifold. We also obtain some characterizations for a GCR-lightlike submanifold to be locally a GCR-lightlike warped produ...