We study the planar problem of two satellites attracted by a center of force. Assuming that the center of mass of the two-satellite system is on a circular orbit around the center of force and using Levi-Civita regularization we prove the existence of an almost periodic orbit with an infinite number of collision between the satellites.

A noncommutative-geometric formalism of framed principal bundles is sketched, in a special case of quantum bundles (over quantum spaces) possessing classical structure groups. Quantum counterparts of torsion operators and Levi-Civita type connections are analyzed. A construction of a natural differential calculus on framed bundles is described. Illustrative examples are presented.

The method based on the Horský-Mitskievitch conjecture is applied to the Levi-Civita vacuum metric. It is shown, that every Killing vector is connected with a particular class of Einstein-Maxwell fields and each of those classes is found explicitly. Some of obtained classes are quite new. Radial geodesic motion in constructed space-times is discussed and graphically illustrated in the Appendix.

Keywords: Non-Archimedean analysis Levi-Civita fields Power series Measure theory and integration Optimization Computational applications This paper is dedicated to the loving memory of my brother Saïd Shamseddine (1968–2013). a b s t r a c t In this paper, we present an overview of some of our research on the Levi-Civita fields R and C. R (resp. C) is the smallest non-Archimedean field extensi...

Finding diffeomorphism-invariant observables to characterize the properties of gravity and spacetime at Planck scale is essential for making progress in quantum gravity. The holonomy Wilson loop Levi-Civita connection are potentially interesting ingredients construction curvature observables. Motivated by recent developments nonperturbative gravity, we establish new relations three four dimensi...

This is a survey of recent contributions to the area of special Kähler geometry. It is based on lectures given at the 21st Winter School on Geometry and Physics held in Srni in January 2001. 1 Remarkable features of special Kähler manifolds A (pseudo-) Kähler manifold (M,J, g) is a differentiable manifold endowed with a complex structure J and a (pseudo-) Riemannian metric g such that (i) J is ...

Riemannian manifolds with a Levi-Civita connection and constant Ricci curvature, or Einstein manifolds, were studied in the works of many mathematicians. This question has been most homogeneous case. In this direction, famous ones are results by D.V. Alekseevsky, M. Wang, V. Ziller, G. Jensen, H.Laure, Y.G. Nikonorov, E.D. Rodionov other At same time, studying little for case an arbitrary metri...

Assume we are given an irreducible matrix P . Recent interest in hyper-algebraically anti-local, additive hulls has centered on extending scalars. We show that |y′′| > π. It is essential to consider that κ may be normal. It would be interesting to apply the techniques of [28] to semi-Artin–Levi-Civita polytopes.

We develop both mathematical models and computational algorithms for variational denoising and restoration of nonflat image features. Nonflat image features are those that live on Riemannian manifolds, instead of on the Euclidean spaces. Familiar examples include the orientation feature (from optical flows or gradient flows) that lives on the unit circle S, the alignment feature (from fingerpri...

For (2+2)–dimensional nonholonomic distributions, the physical information contained into a spacetime (pseudo) Riemannian metric can be encoded equivalently into new types of geometric structures and linear connections constructed as nonholonomic deformations of the Levi–Civita connection. Such deformations and induced geometric/physical objects are completely determined by a prescribed metric ...