We describe the geometry of geodesics on a Lorentz ellipsoid: give explicit formulas for the first integrals (pseudo-confocal coordinates), curvature, geodesically equivalent Riemannian metric, the invariant area-forms on the timeand space-like geodesics and invariant 1-form on the space of null geodesics. We prove a Poncelet-type theorem for null geodesics on the ellipsoid: if such a geodesic ...

Inspired by a recent work Berger, we introduce the concept of pointwise emergence. This provides with new quantitative perspective into study non-existence averages for dynamical systems. We show that high emergence on large set appears abundant systems: Any continuous maps compact metric space specification property have super-polynomial residual subset state space. Furthermore, there is dense...

We study the stability of compact pseudo-Kähler manifolds, i.e. complex manifolds X endowed with a symplectic form compatible structure X. When corresponding metric is positive-definite, Kähler and any sufficiently small deformation admits by well-known result Kodaira Spencer. prove that surfaces are also stable, but we show fails in every dimension n≥3. Similar results obtained for neutral Cal...

Our paper explores warped product pointwise semi-slant submanifolds with a semi-symmetric metric connection in an odd-dimensional sphere and uncovers fundamental results. We also demonstrate how our findings can be applied to the homology of these submanifolds. Notably, we prove that under specific condition, there are no stable currents for This work adds valuable insights into stability behav...

The object of the present paper is to investigate the applications of pseudo cyclic Ricci symmetric manifolds admitting a semi-symmetric metric connection to the general relativity and cosmology.

We prove that a space is a sequentially-quotient (pseudo-sequencecovering), π-image of a separable metric space if and only if it has a point-star network consisting of countable-cs∗-covers. We also investigate spaces with count-

Here shape space is either the manifold of simple closed smooth unparameterized curves in R or is the orbifold of immersions from S to R modulo the group of diffeomorphisms of S. We investige several Riemannian metrics on shape space: L-metrics weighted by expressions in length and curvature. These include a scale invariant metric and a Wasserstein type metric which is sandwiched between two le...

In this lecture we will describe our recent joint work with SimonBrendle ([1], [2]) in which we give the differentiable classification ofcompact Riemannian manifolds with pointwise 1/4-pinched curvature.Our theorems are:Theorem 1. Let M be a compact Riemannian manifold with pointwise1/4-pinched curvature. Then M admits a metric of constant curvature,and therefore is ...

Timed temporal logics encompass a huge diversity of operators, as a result of which, the decidability and expressiveness properties vary considerably. Both pointwise and continuous interpretations of temporal logics can be defined (over finite words), and properties vary based on the interpretation too. The EhrenfeuchtFräıssé games (EF games) for Linear Temporal Logic, as defined by Etessami-Wi...

In this paper some results on fixed point theorems for contractive type fuzzy mappings are obtained in fuzzy quasi-pseudo-metric space which extend and generalize the result of Telci and Sahin [8].