Stochastic Anticipative Integrals on a Riemannian Manifold

On a class of paracontact Riemannian manifold

We classify the paracontact Riemannian manifolds that their Riemannian curvature satisfies in the certain condition and we show that this classification is hold for the special cases semi-symmetric and locally symmetric spaces. Finally we study paracontact Riemannian manifolds satisfying R(X, ξ).S = 0, where S is the Ricci tensor.

on a class of paracontact riemannian manifold

we classify the paracontact riemannian manifolds that their rieman-nian curvature satisfies in the certain condition and we show that thisclassification is hold for the special cases semi-symmetric and locally sym-metric spaces. finally we study paracontact riemannian manifolds satis-fying r(x, ξ).s = 0, where s is the ricci tensor.

Riemannian stochastic variance reduced gradient on Grassmann manifold

Stochastic variance reduction algorithms have recently become popular for minimizing the average of a large, but finite, number of loss functions. In this paper, we propose a novel Riemannian extension of the Euclidean stochastic variance reduced gradient algorithm (R-SVRG) to a compact manifold search space. To this end, we show the developments on the Grassmann manifold. The key challenges of...

On the stochastic Strichartz estimates and the stochastic nonlinear Schrödinger equation on a compact riemannian manifold

We prove the existence and the uniqueness of a solution to the stochastic NSLEs on a two-dimensional compact riemannian manifold. Thus we generalize (and improve) a recent work by Burq et all [11] and a series of papers by de Bouard and Debussche, see e.g. [16, 17] who have examined similar questions in the case of the at euclidean space. We prove the existence and the uniqueness of a local max...

Computing Geodesics on a Riemannian Manifold