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Suppose $(X,J,\omega)$ is a Fano manifold and $t \to r_t$ is a diverging K\"ahler-Ricci trajectory. We construct a bounded geodesic ray $t \to u_t$ weakly asymptotic to $t \to r_t$, along which Ding's $\mathcal F$-functional decreases,…

We investigate the geodesic motions of a massive particle and light ray in the hyperplane orthogonal to the symmetry axis in the 5-dimensional hypercylindrical spacetime. The class of the solutions depends on one constant a which is the…

We characterize real and complex functions which, when applied entrywise to square matrices, yield a positive definite matrix if and only if the original matrix is positive definite. We refer to these transformations as sign preservers.…

In this short paper we introduce a variant of the approach to inverting the X-ray transform that originated in the author's work with Uhlmann. The new method is based on semiclassical analysis and eliminates the need for using sufficiently…

In this paper the space of images is considered as a Riemannian manifold using the metamorphosis approach, where the underlying Riemannian metric simultaneously measures the cost of image transport and intensity variation. A robust and…

We show that on any compact Riemann surface with variable negative curvature there exists a measure which is invariant and ergodic under the geodesic flow and whose projection to the base manifold is 2-dimensional and singular with respect…

We construct explicitly the constants of motion for geodesics in the $5$-dimensional Sasaki-Einstein spaces $Y^{p,q}$. To carry out this task we use the knowledge of the complete set of Killing vectors and Killing-Yano tensors on these…

In (2+1)-dimensional general relativity, the path integral for a manifold $M$ can be expressed in terms of a topological invariant, the Ray-Singer torsion of a flat bundle over $M$. For some manifolds, this makes an explicit computation of…

Let $X$ be a connected compact 3-manifold with non-empty boundary. Consider the boundary $M$ of $X\times D^2$. $M$ is a 4-dimensional closed manifold and has the same fundamental group as $X$. Various examples of $X$ are known for which a…

We evaluate the impact factor of the transition gamma* -> rhoT taking into account the twist 3 contributions. We show that a gauge invariant expression is obtained with the help of QCD equations of motion. Our results are free of end-point…

We study integral transforms mapping a function on the Euclidean space to the family of its integration on some hypersurfaces, that is, a function of hypersurfaces. The hypersurfaces are given by the graphs of functions with fixed axes of…

Let $\bbK=\mathbb R, \mathbb C, \mathbb H$ be the field of real, complex or quaternionic numbers and $M_{p, q}(\bbK)$ the vector space of all $p\times q$-matrices. Let $X$ be the matrix unit ball in $M_{n-r, r}(\bbK)$ consisting of…

To simulate open boundaries within finite computation domain, real-function coordinate transformation in the framework of generally covariant formulation of Maxwell equations is proposed. The mapping--realized with arctangent function…

The geometric concept of geodesic completeness depends on the choice of the metric field or "metric frame". We develop a frame-invariant concept of "generalised geodesic completeness" or "time completeness". It is based on the notion of…

Discrete forms of the mean and directed curvature are constructed on piecewise flat manifolds, providing local curvature approximations for smooth manifolds embedded in both Euclidean and non-Euclidean spaces. The resulting expressions take…

Consider a broken geodesics $\alpha([0,l])$ on a compact Riemannian manifold $(M,g)$ with boundary of dimension $n\geq 3$. The broken geodesics are unions of two geodesics with the property that they have a common end point. Assume that for…

It is shown that any theory of gravitation, based on the hypothesis of the geodesic motion of test particles must be invariant under geodesic (projecive) mappings of the used space-time. The reason is that due to invariance of the equations…

We give a formula for the topological pressure of the geodesic flow of a compact rank 1 manifold in terms of the growth of the number of closed hyperbolic (rank 1) geodesics. We derive an equidistribution result for these geodesics with…

Using variations of Riemannian metric that preserve a given Riemannian submersion, keep its fibers totally geodesic and the metric restricted to the fibers fixed, but change the horizontal distribution, we examine changes of sectional…

In the paper, some concepts of modern differential geometry are used as a basis to develop an invariant theory of mechanical systems, including systems with gyroscopic forces. An interpretation of systems with gyroscopic forces in the form…