arXiv subjects

Rafik Nasri

Publications and source records attributed to Rafik Nasri.

3 recordsLinked to original sources

arXiv2015

Product of statistical manifolds with a non-diagonal metric

In this paper, we generalize the dualistic structures on warped product manifolds to the dualistic structures on generalized warped product manifolds. we develop an expression of curvature for the connection of the generalized warped product in relation to those corresponding analogues of its base and fiber and warping functions. we show that the dualistic structures on the base $M_{_1}$ and the fiber $M_{_2}$ induces a dualistic structure on the generalized warped product $M_1\times M_2$ and conversely, moreover, $(M_{_1}\times M_{_1},G_{_{f_{_1}f_{_2}}})$ or $(M_{_1}\times M_{_1},\tilde{g}_{_{f_{_1}f_{_2}}})$ is statistical manifold if and only if $(M_{_1},g_{_1})$ and $(M_{_1},g_{_1})$ are. Finally, Some interesting consequences are also given.

math.DG↗

arXiv2015

Non-diagonal metric on a product riemanniann manifold

In this paper, We construct the symmetric tensor field $G_{f_1f_2}$ and $h_{f_1f_2}$ on a product manifold and we give conditions under which $G_{f_1f_2}$ becomes a metric tensor, theses tensors fields will be called the generalized warped product, and then we develop an expression of curvature for the connection of the generalized warped product in relation to those corresponding analogues of its base and fiber and warping functions. By constructing a frame field in $M_1\times_{f_1f_2}M_2$ with respect to the Riemannian metric $G_{f_1f_2}$ and $h_{f_1f_2}$, then we calculate the Laplacian$-$Beltrami operator of a function on a generalized warped product which may be expressed in terms of the local restrictions of the functions to the base and fiber. Finally, we conclude some interesting relationships between the geometry of the couples $(M_1,g_1)$ and $(M_2,g_2)$ and that of $(M_1\times M_2,h_{f_1f_2})$.

math.DG↗

arXiv2015

Warped Poisson Brackets on Warped Products

In this paper, we generalize the geometry of the product pseudo-Riemannian manifold equipped with the product Poisson structure (\cite{Nas2}) to the geometry of a warped product of pseudo-Riemannian manifolds equipped with a warped Poisson structure. We construct three bivector fields on a product manifold and show that each of them lead under certain conditions to a Poisson structure. One of these bivector fields will be called the warped bivector field. For a warped product of pseudo-Riemannian manifolds equipped with a warped bivector field, we compute the corresponding contravariant Levi-Civita connection and the curvatures associated with.

math.DG↗