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...

Three dimensional topologically massive gravity (TMG) with a negative cosmological constant −l−2 and positive Newton constant G admits an AdS3 vacuum solution for any value of the graviton mass μ. These are all known to be perturbatively unstable except at the recently explored chiral point μl = 1. However we show herein that for every value of μl 6= 3 there are two other (potentially stable) v...

In this paper, by supposing a natural comparison inequality on the positive r-th mean curvatures of the hypersurface, we obtain some new Bernstein-type theorems for complete spacelike hypersurfaces immersed in a semi-Riemannian warped product of constant sectional curvature. Generalizing the above results, under a restriction on the sectional curvature or the Ricci curvature tensor of the fiber...

We consider Einstein hypersurfaces of warped products $$I\times _\omega {\mathbb {Q}}_\epsilon ^n,$$ where $$I\subset {R}}$$ is an open interval and $${\mathbb ^n$$ the simply connected space form dimension $$n\ge 2$$ constant sectional curvature $$\epsilon \in \{-1,0,1\}$$ . show that, for all $$c\in (resp. $$c>0$$ ), there exist rotational c in {H}}^n$$ {R}}^n$$ {S}}^n$$ provided that $$\omeg...

In this paper, we have studied warped products and multiply warped product on quasi-Einstein manifold with semi-symmetric nonmetric connection. Then we have applied our results to generalized Robertson-Walker space times with a semi-symmetric non-metric connection.