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We prove results toward classifying compact Lorentz manifolds on which Heisenberg groups act isometrically. We give a general construction, leading to a new example, of codimension-one actions—those...
We prove a structure theorem for compact aspherical Lorentz manifolds with abundant local symmetry. If M is a compact, aspherical, real-analytic, complete Lorentz manifold such that the isometry grou...
A Margulis spacetime is a complete affine 3-manifold M with nonsolvable fundamental group. Associated to every Margulis spacetime is a noncompact complete hyperbolic surface S. We show that eve...
Motivated by Felix Klein’s notion that geometry is governed by its group of symmetry transformations, Charles Ehresmann initiated the study of geometric structures on topological spaces locally model...
We introduce the notion of recurrent geodesic rays in a complete °at Lorentz 3-manifold. We completely classify the dynamical behavior of geodesics in cyclic quotients, and apply this classiˉcation...
This paper is the sequel to The radiance obstruction and par- allel forms on a;ffne manifolds (lYans. Amer. Math. Soc. 286 (1984), 629 649) which introduced a new family of secondary characteristi...
A manifold M is affine if it is endowed with a distinguished atlas whose coordinate changes are locally affine. When they are locally linear M is called radiant. The obstruction to radiance is a o...
TWO EXAMPLES OF AFFINE MANIFOLDS     AFFINE MANIFOLDS  affine       2015/9/29
An affine manifold is a manifold with a distinguished system of affine coordinates, namely, an open covering by charts which map homeomorphically onto open sets in an affine space E such that on ov...
It is well known that the real cohomology of a compact Riemannian manifold M is isomorphic to the algebra of its harmonic forms. When M is a fiat Riemannian manifold, i.e. a Euclidean manifold, a ...
We prove two-sided estimates of heat kernels on non-parabolic Riemannian manifolds with ends, assuming that the heat kernel on each end separately satisfies the Li-Yau estimate. Résumé. — Nous obte...
Given a Riemannian manifold (M, g), we study the solutions of heat equations associated with second order differential operators in divergence form that are uniformly elliptic with respect to g . Ty...
The task of constructing higher-dimensional invariant manifolds for dynamical systems can be computationally expensive. We demonstrate that this problem can be locally reduced to solving a system of...
Recently, the Isomap procedure [1] was proposed as a new way to recover a low-dimensional parametrization of data lying on a low-dimensional submanifold in high-dimensional space. The method assumes...

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