on a class of paracontact 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...

Computing Geodesics on a Riemannian Manifold

Sobolev Metrics on the Riemannian Manifold of All Riemannian Metrics

On the manifold M(M) of all Riemannian metrics on a compact manifold M one can consider the natural L-metric as decribed first by [10]. In this paper we consider variants of this metric which in general are of higher order. We derive the geodesic equations, we show that they are well-posed under some conditions and induce a locally diffeomorphic geodesic exponential mapping. We give a condition...

Sobolev Norms of Eigenfunctions on a Closed Riemannian Manifold Sobolev Norms of Eigenfunctions on a Closed Riemannian Manifold

Let χλ (cf (1.1)) be the unit spectral projection operator with respect to the Laplace-Beltrami operator ∆ on a closed Riemannian manifold M . We generalize the (L2, L∞) estimate of χλ by Hörmander [3] to those of covariant derivatives of χλ Moreover we extend the (L2, Lp) estimates of χλ by Sogge [7] [8] to (L2, Sobolev Lp) estimates of χλ.

Some vector fields on a riemannian manifold with semi-symmetric metric connection

In the first part of this paper, some theorems are given for a Riemannian manifold with semi-symmetric metric connection. In the second part of it, some special vector fields, for example, torse-forming vector fields, recurrent vector fields and concurrent vector fields are examined in this manifold. We obtain some properties of this manifold having the vectors mentioned above.