In this paper we study a Riemanian metric on the tangent bundle T (M) of a Riemannian manifold M which generalizes Sasaki metric and Cheeger Gromoll metric and a compatible almost complex structure which together with the metric confers to T (M) a structure of locally conformal almost Kählerian manifold. This is the natural generalization of the well known almost Kählerian structure on T (M). W...

Ionic liquids (ILs) are salts with low melting point close to room temperature. They have interesting solvent properties and are able to dissolve some polar molecules. Polyvinyl formal-IL (1-Ethyl-3methylimidazoliumtosylate) nanocomposite electrolyte with layered filler was synthesized by solution cast technique. Changes in surface morphology have been observed using optical microscopy and scan...

In this note, we show that the holonomy group of a Riemannian connection on a k-dimensional Euclidean vector bundle is transitive on the unit sphere bundle whenever the Euler class χ is spherical. We extract several consequences from this, among them that this is always the case as long as χ does not vanish, and the base of the bundle is simply connected and rationally (k + 1)/2-connected.

We introduce the concepts of second-order radial composed tangent derivative, second-order radial tangent derivative, second-order lower radial composed tangent derivative, and second-order lower radial tangent derivative for set-valued maps by means of a radial tangent cone, second-order radial tangent set, lower radial tangent cone, and second-order lower radial tangent set, respectively. Som...

In this study, we give the relationships between the conical curvatures of ruled surfaces generated by the unit vectors of the ruling, central normal and central tangent of a ruled surface in the Euclidean 3-space E^3. We obtain differential equations characterizing slant ruled surfaces and if the reference ruled surface is a slant ruled surface, we give the conditions for the surfaces generate...

Contents 1. Introduction 2 1.1. Equidistribution theorems for closed geodesics 2 1.2. The modular surface 3 1.3. Results 5 1.4. Remarks 7 1.5. Plan of the paper 9 1.6. Acknowledgments 9 2. Background on periods 9 2.1. The upper half-plane and its unit tangent bundle 9 2.2. Quotients 11 2.3. A correspondence with binary quadratic forms 12 2.4.

We show that the unit tangent bundle of S4 and a real cohomology CP 3 admit Riemannian metrics with positive sectional curvature almost everywhere. These are the only examples so far with positive curvature almost everywhere that are not also known to admit positive curvature. AMS Classi cation numbers Primary: 53C20 Secondary: 53C20, 58B20, 58G30