Reputation
649
Next privilege 1,000 Rep.
See votes, expandable usercard
Badges
3 13
Newest
 Yearling
Impact
~10k people reached

  • 0 posts edited
  • 0 helpful flags
  • 29 votes cast
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
Let us continue this discussion in chat.
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.