Oliver Jones
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 Jan 21 comment Compact Riemann manifolds with constant injectivity radius Yes, if it's thin enough. Jan 21 comment Compact Riemann manifolds with constant injectivity radius @DouglasZare Nice observation. That means a torus of revolution is such an example. Jan 21 comment Compact Riemann manifolds with constant injectivity radius Actually, there's a simpler example. The torus of revolution in $\Bbb{R}^3$ has the property that $\text{inj}_p$ is the same for all points $p$. Jan 20 comment Compact Riemann manifolds with constant injectivity radius @WłodzimierzHolsztyński It's an infimum. Jan 20 comment Compact Riemann manifolds with constant injectivity radius I'll take a look at your suggestion. Thanks. Jan 20 comment Compact Riemann manifolds with constant injectivity radius So the condition doesn't characterize homogeneous manifolds. Does it imply anything? Jan 20 comment Compact Riemann manifolds with constant injectivity radius But what can we say about manifolds with this property? Jan 20 comment Compact Riemann manifolds with constant injectivity radius @WłodzimierzHolsztyński Let $\gamma$ be a geodesic starting at $p$ and let $B=$sup$\{b>0 : \gamma_{[0, b]}$ is minimizing$\}$. If $B< \infty$, we call $q=\gamma(B)$ the cut point of $p$ along $\gamma$. The cut locus of $p$ is the set of all points $q$ such that $q$ is the cut point of $p$ along some geodesic. Jan 20 comment Compact Riemann manifolds with constant injectivity radius No I don't, I'm afraid. It's a necessary condition that came up while studying a problem. I know that homogeneous manifolds have this property but to what extent does it characterize them? Jan 20 asked Compact Riemann manifolds with constant injectivity radius Jan 20 asked Flows associated with Killing fields Jan 19 awarded Yearling Jan 19 comment Are there infinite constructions for partial circulant hadamard matrices? @dorothy I'm the same person! Should I change my se name? Jan 19 answered Are there infinite constructions for partial circulant hadamard matrices? Jan 12 revised Geodesic Digons in Reductive Spaces added 89 characters in body Jan 8 comment Geodesic Digons in Reductive Spaces Jan 8 comment Geodesic Digons in Reductive Spaces It's not the case that all geodesics in a NRSPC are closed. Jan 8 comment Geodesic Digons in Reductive Spaces No, I'm not saying that. I'm allowing digons which consist of two closed geodesics joined at a point. Jan 8 comment Geodesic Digons in Reductive Spaces The second vertex is also the north pole. I'm allowing for digons which don't have distinct vertices. Jan 7 comment Geodesic Digons in Reductive Spaces I don't think you're correct here: the real projective space is a symmetric space and so all conjugate points are isotropic. By the way, any simply connected manifold is automatically orientable.