This survey is dedicated to Professor Anatole Katok on the occasion of his sixtieth birthday.
He has made numerous important contributions to dynamics and ergodic theory proper …

New Examples of Manifolds with Completely Page 1 ADVANCES IN MATHEMATICS 108,
34(y366 (1994) New Examples of Manifolds with Completely Integrable Geodesic Flows GP …

A Riemannian manifold (M^ nn, g) is said to be the center of thecomplex manifold X^ nn if M
is the zero set of a smooth strictly plurisubharmonic exhaustion function ν 2 on X such that ν …

In this paper we give a characterization of locally compact rank one symmetric spaces,
which can be seen as an analogue of Ballmann's and Burns and Spatzier's …

We discuss the rigidity (or lack thereof) imposed by different notions of having an abundance
of zero curvature planes on a complete Riemannian $3 $-manifold. We prove a rank rigidity …

We introduce a notion of the Euclidean and the Minkowski rank for arbitrary metric spaces
and we study their behaviour with respect to products. We show that the Minkowski rank is …

This paper presents hyperbolic rank rigidity results for rank 1, nonpositively curved spaces.
Let $ M $ be a compact, rank 1 manifold with nonpositive sectional curvature and suppose …

Let M be a complete irreducible Riemannian manifold. A k-flat in M is a complete connected
flat totally geodesic immersed submanifold of dimension k. The rank of M is the maximal …

Rigidity results are obtained for Riemannian d-manifolds with sec> 1 and spherical rank at
least d 2> 0. Conjecturally, all such manifolds are locally isometric to a round sphere or …

Hyperbolic rank rigidity for manifolds of -pinched negative curvature Page 1 Ergod. Th. & Dynam.
Sys. (2020), 40, 1194–1216 doi:10.1017/etds.2018.113 c Cambridge University Press, 2018 …