This foliation is nonorientable and it has a transversal measure. The measure can be given locally out of the singularities by a closed 1-form. Half translation surfaces. Let M be a two-dimensional surface with a flat metric which has only conical singularities. The surface is called a half translation if the holonomy along any path on the surface is either Id or -Id. It is clear that the angle...

Consider a compact Riemannian manifold (M, g) with metric g and dimension n ≥ 3. The Schouten tensor Ag associated with g is a symmetric (0, 2)-tensor field describing the non-conformally-invariant part of the curvature tensor of g. In this paper, we consider the elementary symmetric functions {σk(Ag), 1 ≤ k ≤ n} of the eigenvalues of Ag with respect to g; we call σk(Ag) the k-th Schouten curva...

Warped products provide a rich class of physically significant geometric objects. Warped product construction is an important method to produce a new metric with a base manifold and a fibre. We construct compact base manifolds with a positive scalar curvature which do not admit any non-trivial quasi-Einstein warped product, and non compact complete base manifolds which do not admit any non-triv...

In this note, we announce some results showing unexpected similarities between the moduli spaces of constant curvature metrics on 2-manifolds (the Riemann moduli space) and moduli spaces of Einstein metrics on 4manifolds. Let J? denote the moduli space of Einstein metrics of volume 1 on a compact, orientable 4-manifold M. If J£\ denotes the space of smooth Riemannian metrics of volume 1 on M, e...

Given a compact and connected metric space (continuum) X, we study topological and dynamical properties of the hyperspace of normal fuzzy sets F1(X) equipped with the Hausdorff, endograph or sendograph metric. Among the many results we show that it is contractible, path connected, locally contractible, locally path connected, locally simply connected and locally connected. For the endograph met...

We propose a notion of continuous path for locally finite metric spaces, taking inspiration from the recent development of A-theory for locally finite connected graphs. We use this notion of continuity to derive an analogue in Z of the Jordan curve theorem and to extend to a quite large class of locally finite metric spaces (containing all finite metric spaces) an inequality for the l-distortio...

We show that the " Taub-bolt instantons " are the only Riemannian, Ricci-flat and asymptotically locally flat (ALF) C 2-metrics on a 4-dimensional, complete, simply connected man-ifold having (at least) a one-parameter group of isometries which are compatible with ALF, have trajectories of bounded length at infinity and no isolated fixed points. Attempts of estimating the path integral of Quant...

We prove a simple, explicit formula for the mass of any asymptotically locally Euclidean (ALE) Kähler manifold, assuming only the sort of weak fall-off conditions required for the mass to actually be well-defined. For ALE scalar-flat Kähler manifolds, the mass turns out to be a topological invariant, depending only on the underlying smooth manifold, the first Chern class of the complex structur...

Every Finsler metric naturally induces a spray but not so for the converse. The notion sprays of scalar (resp. isotropic) curvature has been known as generalization metrics flag curvature. In this paper, new notion, constant curvature, is introduced and especially it shows that isotropic necessarily even in dimension $$n\ge 3$$ . Further, complete conditions are given constant) to be metrizable...