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This lecture concerns the metric Riemannian geometry of Einstein manifolds, which is a central theme in modern differential geometry and is deeply connected to a large variety of fundamental problems ...
I will present the joint work with Jialun Li and Pratyush Sarkar in the talk. As a final work to establish that the frame flows for geometrically finite hyperbolic manifolds of arbitrary dimensions ar...
The object of this week is to bring together specialists in the domains of Riemannian geometry, low-dimensional topology and geometric group theory to take stock of current interactions and encourage ...
As one of most important objects in mathematics, ‘manifold’ has provided us more and more insights and benefits. In the past half century, more and more different areas in mathematics have been inters...
We study conformal actions of connected nilpotent Lie groups on compact pseudo-Riemannian manifolds. We prove that if a type-(p,q) compact manifold M supports a conformal action of a connected nilpo...
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...
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 ...
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...
Chow and Hamilton introduced the cross curvature flow on closed 3- manifolds with negative or positive sectional curvature. In this paper, we study the negative cross curvature flow in t...
Some invariant tensors in two Naveira classes of Riemannian product manifolds are considered. These tensors are related with natural connections, i.e. linear connections preserving the Riemannian metr...

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