The object of the present paper is to characterize K-contact Einstein manifolds satisfying the curvature condition R · C = Q(S,C), where C is the conformal curvature tensor and R the Riemannian curvature tensor. Next we study K-contact Einstein manifolds satisfying the curvature conditions C ·S = 0 and S ·C = 0, where S is the Ricci tensor. Finally, we consider K-contact Einstein manifolds sati...

When Einstein was thinking about the theory of general relativity based on the elimination of especial relativity constraints (especially the geometric relationship of space and time), he understood the first limitation of especial relativity is ignoring changes over time. Because in especial relativity, only the curvature of the space was considered. Therefore, tensor calculations should be to...

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.

Here, a Finsler manifold $(M,F)$ is considered with corresponding curvature tensor, regarded as $2$-forms on the bundle of non-zero tangent vectors. Certain subspaces of the tangent spaces of $M$ determined by the curvature are introduced and called $k$-nullity foliations of the curvature operator. It is shown that if the dimension of foliation is constant, then the distribution is involutive...

here, a finsler manifold $(m,f)$ is considered with corresponding curvature tensor, regarded as $2$-forms on the bundle of non-zero tangent vectors. certain subspaces of the tangent spaces of $m$ determined by the curvature are introduced and called $k$-nullity foliations of the curvature operator. it is shown that if the dimension of foliation is constant, then the distribution is involutive a...

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.

Let us define a curvature invariant of the order k as a scalar polynomial constructed from gαβ, the Riemann tensor Rαβγδ, and covariant derivatives of the Riemann tensor up to the order k. According to this definition, the Ricci curvature scalar R or the Kretschmann curvature scalar RαβγδR αβγδ are curvature invariants of the order zero and Rαβγδ;εR αβγδ;ε is a curvature invariant of the order ...

We obtain the evolution equations for the Riemann tensor, the Ricci tensor and the scalar curvature induced by the mean curvature flow. The evolution for the scalar curvature is similar to the Ricci flow, however, negative, rather than positive, curvature is preserved. Our results are valid in any dimension.

Tensor voting is an efficient algorithm for perceptual grouping and feature extraction, particularly for contour extraction. In this paper two studies on tensor voting are presented. First the use of iterations is investigated, and second, a new method for integrating curvature information is evaluated. In opposition to other grouping methods, tensor voting claims the advantage to be non-iterat...

In this paper, we are interested in certain global geometric quantities associated to the Schouten tensor and their relationship in conformal geometry. For an oriented compact Riemannian manifold (M,g) of dimension n > 2, there is a sequence of geometric functionals arising naturally in conformal geometry, which were introduced by Viaclovsky in [29] as curvature integrals of Schouten tensor. If...