The space of full-ranked one-forms on a smooth, orientable, compact manifold (possibly with boundary) is metrically incomplete respect to the induced geodesic distance generalized Ebin metric. We show equality between distances metric and corresponding Riemannian defined each fiber. Using this result, we immediately have concrete description completion one-forms. Additionally, study relationshi...

Several researchers proposed using non-Euclidean metrics on point sets in Euclidean space for clustering noisy data. Almost always, a distance function is desired that recognizes the closeness of the points in the same cluster, even if the Euclidean cluster diameter is large. Therefore, it is preferred to assign smaller costs to the paths that stay close to the input points. In this paper, we c...

The Ruelle zeta-function of the geodesic flow on the sphere bundle S(X) of an even-dimensional compact locally symmetric space X of rank 1 is a meromorphic function in the complex plane that satisfies a functional equation relating its values in s and -s . The multiplicity of its singularity in the central critical point 5 = 0 only depends on the hyperbolic structure of the flow and can be calc...

the sequential $p$-convergence in a fuzzy metric space, in the sense of george and veeramani, was introduced by d. mihet as a weaker concept than convergence. here we introduce a stronger concept called $s$-convergence, and we characterize those fuzzy metric spaces in which convergent sequences are $s$-convergent. in such a case $m$ is called an $s$-fuzzy metric. if $(n_m,ast)$ is a fuzzy metri...

The interior of every compact contractible PL n-manifold (n 5) supports a complete geodesic metric of strictly negative curvature. This provides a new family of simple examples illustrating the negative answer to a question of M. Gromov which asks whether metrically convex geodesic spaces which are topological manifolds must be homeomorphic to Euclidean spaces. The rst examples verifying the ne...

We present the ‘Basic S*’ algorithm for computing shortest path through a metric simplicial complex. In particular, given a metric graph, G, which is constructed as a discrete representation of an underlying configuration space (a larger “continuous” space/manifold typically of dimension greater than one), we consider the Rips complex, R(G), associated with it. Such a complex, and hence shortes...

Given a hyperbolic 3-manifold containing an embedded geodesic, we estimate the volume of a complete hyperbolic metric after drilling the geodesic from the manifold in terms of the radius of an embedded tube about the geodesic.

1. If the geodesic ow of a metric G on the torus T 2 is quadrati-cally integrable then the torus T 2 isometrically covers a torus with a Liouville metric on it. 2. The set of quadratically integrable geodesic ows on the Klein bottle is described. x1. Introduction Let M 2 be a smooth close surface with a Riemannian metric G on it. The metric allows to canonically identify the tangent and the co-...

For the gravitational wave model based on type III Shapovalov space-time, test particle trajectories and exact solution of geodesic deviation equations for Bianchi VII universe are obtained. Based found 4-vector deviation, tidal accelerations in a calculated. obtained privileged coordinate system, an explicit form transformations into synchronous reference system is found, which allows time syn...

A criterion in terms of differential invariants for a metric on a surface to be Liouville is established. Moreover, in this paper we completely solve in invariant terms the local mobility problem of a 2D metric, considered by Darboux: How many quadratic in momenta integrals does the geodesic flow of a given metric possess? The method is also applied to recognition of other polynomial integrals ...