The standard eigenfunctions φλ = ei〈λ,x〉 on flat tori Rn/L have L-norms bounded independently of the eigenvalue. In the case of irrational flat tori, it follows that L2normalized eigenfunctions have uniformly bounded L-norms. Similar bases exist on other flat manifolds. Does this property characterize flat manifolds? We give an affirmative answer for compact Riemannian manifolds with quantum co...

For any ε > 0, we construct an explicit smooth Riemannian metric on the sphere Sn, n ≥ 3, that is within ε of the round metric and has a geodesic for which the corresponding orbit of the geodesic flow is ε-dense in the unit tangent bundle. Moreover, for any ε > 0, we construct a smooth Riemannian metric on S, n ≥ 3, that is within ε of the round metric and has a geodesic for which the complemen...

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...

ELECTRON MICROSCOPIC STUDY OF THE GOLGI ZONE OF THE RAT SPERMATIDS REVEALED TWO MAIN TYPES OF VESICULAR STRUCTURES: flat vesicles generally accumulated in stacks and spheroidal vesicles of various sizes. The Golgi zone of young spermatids showed a predominance of flat vesicles and small spherical vesicles, while the "residual" Golgi zone of the maturing spermatids displayed an increased number ...

3D reconstructions allow cultural institutions such as museums and historic sites a tool to vividly illustrate the past while educating the public about competing interpretations of history and change over time. 3D technology also offers many practical benefits including low cost, flexibility, and the potential for collaboration. This paper presents potential applications of 3D reconstructions ...

Mosaicing of images is the task of fusing a collection of images with smaller elds of view to obtain an image with a larger eld of view. In order to accomplish this task, images should be geometrically and radio-metrically corrected. We propose a new approach for perspective correction useful when smaller images are gathered by rotating a camera with a xed position. These images are projected o...

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.