Monge’s transport problem 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.

Evolution of the first eigenvalue of buckling problem on Riemannian manifold under Ricci flow

Among the eigenvalue problems of the Laplacian, the biharmonic operator eigenvalue problems are interesting projects because these problems root in physics and geometric analysis. The buckling problem is one of the most important problems in physics, and many studies have been done by the researchers about the solution and the estimate of its eigenvalue. In this paper, first, we obtain the evol...

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.

A quadratic Bolza-type problem in a Riemannian manifold

A classical nonlinear equation Ds ’ x þrxVðx; sÞ 1⁄4 0 on a complete Riemannian manifoldM is considered. The existence of solutions connecting any two points x0; x1AM is studied, i.e., for T40 the critical points of the functional JT ðxÞ 1⁄4 12 R T 0 / ’ x; ’ xS ds R T 0 Vðx; sÞds with xð0Þ 1⁄4 x0; xðTÞ 1⁄4 x1: When the potential V has a subquadratic growth with respect to x; JT admits a minimu...

Computing Geodesics on a Riemannian Manifold