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Jayq
Jayq
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According to Gromoll and Meyer:

  • Let M be a complete non-compact Riemannian manifold of positive sectional curvature. Then M is diffeomorphic to $\mathbb{R}^n$.

Thus, I think to classify non-compact Riemannian manifolds of positive curvature up to isometry, it suffices to seek for metrics of positive curvature on euclidean spaces. I did some search to find some results related to this problem, but I found few ones.

Therefore, I would be very thankful if give me some information, or/and introduce me some references about metrics of positive curvature on $\mathbb{R}^n$.

According to Gromoll and Meyer:

  • Let M be a complete non-compact Riemannian manifold of positive sectional curvature. Then M is diffeomorphic to $\mathbb{R}^n$.

Thus, I think to classify non-compact Riemannian manifolds up to isometry, it suffices to seek for metrics of positive curvature on euclidean spaces. I did some search to find some results related to this problem, but I found few ones.

Therefore, I would be very thankful if give me some information, or/and introduce me some references about metrics of positive curvature on $\mathbb{R}^n$.

According to Gromoll and Meyer:

  • Let M be a complete non-compact Riemannian manifold of positive sectional curvature. Then M is diffeomorphic to $\mathbb{R}^n$.

Thus, I think to classify non-compact Riemannian manifolds of positive curvature up to isometry, it suffices to seek for metrics of positive curvature on euclidean spaces. I did some search to find some results related to this problem, but I found few ones.

Therefore, I would be very thankful if give me some information, or/and introduce me some references about metrics of positive curvature on $\mathbb{R}^n$.

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Peter Michor
Peter Michor
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According to Gromoll and Meyer:

Let M be a complete non-compact Riemannian manifold of positive sectional curvature. Then M is diffeomorphic to \mathbb{R}^n.
  • Let M be a complete non-compact Riemannian manifold of positive sectional curvature. Then M is diffeomorphic to $\mathbb{R}^n$.

Thus, I think to classify non-compact Riemannian manifolds up to isometry, it suffices to seek for metrics of positive curvature on euclidean spaces. I did some search to find some results related to this problem, but I found few ones.

Therefore, I would be very thankful if give me some information, or/and introduce me some references about metrics of positive curvature on \mathbb{R}^n$\mathbb{R}^n$.

According to Gromoll and Meyer:

Let M be a complete non-compact Riemannian manifold of positive sectional curvature. Then M is diffeomorphic to \mathbb{R}^n.

Thus, I think to classify non-compact Riemannian manifolds up to isometry, it suffices to seek for metrics of positive curvature on euclidean spaces. I did some search to find some results related to this problem, but I found few ones.

Therefore, I would be very thankful if give me some information, or/and introduce me some references about metrics of positive curvature on \mathbb{R}^n.

According to Gromoll and Meyer:

  • Let M be a complete non-compact Riemannian manifold of positive sectional curvature. Then M is diffeomorphic to $\mathbb{R}^n$.

Thus, I think to classify non-compact Riemannian manifolds up to isometry, it suffices to seek for metrics of positive curvature on euclidean spaces. I did some search to find some results related to this problem, but I found few ones.

Therefore, I would be very thankful if give me some information, or/and introduce me some references about metrics of positive curvature on $\mathbb{R}^n$.

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Jayq
Jayq
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non compact riemannian manifolds

According to Gromoll and Meyer:

Let M be a complete non-compact Riemannian manifold of positive sectional curvature. Then M is diffeomorphic to \mathbb{R}^n.

Thus, I think to classify non-compact Riemannian manifolds up to isometry, it suffices to seek for metrics of positive curvature on euclidean spaces. I did some search to find some results related to this problem, but I found few ones.

Therefore, I would be very thankful if give me some information, or/and introduce me some references about metrics of positive curvature on \mathbb{R}^n.