Heat Semigroup on a Complete 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.

Computing Geodesics on a Riemannian Manifold

Approximation of the Heat Kernel on a Riemannian Manifold Based on the Smolyanov–Weizsäcker Approach

Let M be a compact Riemannian manifold without boundary isometrically embedded into Rm, WM,t be the distribution of a Brownian bridge starting at x ∈M and returning to M at time t. Let Qt : C(M)→ C(M), (Qtf)(x) = ∫ C([0,1],Rm) f(ω(t))W x M,t(dω), and let P = {0 = t0 < t1 < · · · < tn = t} be a partition of [0, t]. It was shown in [2] that Qt1−t0 · · ·Qtn−tn−1f → e−t ∆M 2 f , as |P| → 0, (1) in ...

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.