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Jan
21 |
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Compact Riemann manifolds with constant injectivity radius
Yes, if it's thin enough. |
Jan
21 |
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Compact Riemann manifolds with constant injectivity radius
@DouglasZare Nice observation. That means a torus of revolution is such an example. |
Jan
21 |
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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 |
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Compact Riemann manifolds with constant injectivity radius
@WłodzimierzHolsztyński It's an infimum. |
Jan
20 |
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Compact Riemann manifolds with constant injectivity radius
I'll take a look at your suggestion. Thanks. |
Jan
20 |
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Compact Riemann manifolds with constant injectivity radius
So the condition doesn't characterize homogeneous manifolds. Does it imply anything? |
Jan
20 |
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Compact Riemann manifolds with constant injectivity radius
But what can we say about manifolds with this property? |
Jan
20 |
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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 |
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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 |
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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 |
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Geodesic Digons in Reductive Spaces
Let us continue this discussion in chat. |
Jan
8 |
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Geodesic Digons in Reductive Spaces
It's not the case that all geodesics in a NRSPC are closed. |
Jan
8 |
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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 |
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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 |
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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. |