R. Spatzier

activity

19922025

most citedTotally non-symplectic Anosov actions on tori and nilmanifolds

10 citations · 28 across the 23 of their papers we have counts for

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5 papers · 1 filter

math.DG2024

Rigidity of compact rank one symmetric spaces

Chris Connell, Mitul Islam, Thang Nguyen +1

We consider rigidity properties of compact symmetric spaces $X$ with metric $g_{0}$ of rank one. Suppose $g$ is another Riemannian metric on $X$ with sectional curvature $κ$ bounded…

math.DG2018

Almost Isotropic Kaehler Manifolds

Benjamin Schmidt, Krishnan Shankar, Ralf Spatzier

Let $M$ be a complete Riemannian manifold and suppose $p \in M$ . For each unit vector $v \in T_{p} M$ , the $Jacobi operator$ , $J_{v} : v^{⊥} \to v^{⊥}$ is…

math.DG2017★ 2 cited

Hyperbolic rank rigidity for manifolds of $\frac{1}{4}$ -pinched negative curvature

Chris Connell, Thang Nguyen, Ralf Spatzier

A Riemannian manifold $M$ has higher hyperbolic rank if every geodesic has a perpendicular Jacobi field making sectional curvature -1 with the geodesic. If in addition, the section…

math.DG2014

Positively curved manifolds with large spherical rank

Benjamin Schmidt, Krishnan Shankar, Ralf Spatzier

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…

math.DG2003

Spherical rank rigidity and Blaschke manifolds

Krishnan Shankar, Ralf Spatzier, Burkhard Wilking

Let M be a complete Riemannian manifold whose sectional curvature is bounded above by 1. We say that M has positive spherical rank if along every geodesic one hits a conjugate poin…