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A geometric theory for spacetimes whose world lines associated with physical particles have an upper bound for the proper acceleration is developed. After some fundamental remarks on the requirements that the classical dynamics for point…

We construct a first order Lagrangian formalism for bimetric theories with an interaction which is a general function of metrics and their derivatives, including non-analytic functions. The first-order actions are fully equivalent to the…

The M-relative distance, denoted by \rho_M is a generalization of the p-relative distance, which was introduced by Ren-Cang Li. We establish necessary and sufficient conditions under which \rho_M is a metric. In two special cases we derive…

Lipman et al. [ACM Transactions on Graphics 29 (3) (2010), 1--11] introduced the concept of biharmonic distance to measure the distances between pairs of points on a 3D surface. Biharmonic distance has some advantages over resistance…

In many robotics applications, it is necessary to compute not only the distance between the robot and the environment, but also its derivative - for example, when using control barrier functions. However, since the traditional Euclidean…

Manifolds have uses throughout and beyond Mathematics and it is not surprising that topologists have expended a huge effort in trying to understand them. In this article we are particularly interested in the question: `when is a manifold…

Following the general principles of noncommutative geometry, it is possible to define a metric on the space of pure states of the noncommutative algebra generated by the coordinates. This metric generalizes the usual Riemannian one. We…

In Euclidean spaces, the geometric notions of nearest-points map, farthest-points map, Chebyshev set, Klee set, and Chebyshev center are well known and well understood. Since early works going back to the 1930s, tremendous theoretical…

In this paper, we prove that two different observers don't equally measure the distance between two points A and B. For this, we introduce some postulates and obtain a new formula to show distance between A and B. In this formula, radius of…

Distance transformation is an image processing technique used for many different applications. Related to a binary image, the general idea is to determine the distance of all background points to the nearest object point (or vice versa). In…

A way to obtain a correspondence between the first order and second order formalism is studied. By introducing a Lagrange multiplier coupled to the covariant derivative of the metric, a metricity constraint is implemented. The new…

Riemannian metric learning is an emerging field in machine learning, unlocking new ways to encode complex data structures beyond traditional distance metric learning. While classical approaches rely on global distances in Euclidean space,…

Metrics in Grassmannians, or distances between subspaces of same dimension, have many uses, and extending them to the Total Grassmannian of subspaces of different dimensions is an important problem, as usual extensions lack good properties…

Some geometric structures with associated Riemannian metrics have been considered in the book.

The aim of the present article is to give an introduction to the concept of quasi-unitary equivalence and to define several (pseudo-)metrics on the space of self-adjoint operators acting possibly in different Hilbert spaces. As some of the…

Here, it is introduced a concept of convolution metric in Finslerian Geometry. This convolution metric is a kind of function obtained by a given mathematical operation between two Finslerian metrics. Some basic properties of the Finslerian…

We investigate connections between pairs of (pseudo-)Riemannian metrics whose sum is a (tensor) product of a covector field with itself. A bijective mapping between the classes of Euclidean and Lorentzian metrics is constructed as a special…

In this paper, an evidential distance measure is proposed which can measure the difference or dissimilarity between complex basic belief assignments (CBBAs), in which the CBBAs are composed of complex numbers. When the CBBAs are degenerated…

When are two collider events similar? Despite the simplicity and generality of this question, there is no established notion of the distance between two events. To address this question, we develop a metric for the space of collider events…

The metric Mahler measure was first studied by Dubickas and Smyth in 2001 as a means of phrasing Lehmer's conjecture in topological language. More recent work of the author examined a parametrized family of generalized metric Mahler…