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C.F.G
C.F.G
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Sorry if this question is belongs to MSE. I have no idea about it.

Question: Is there any Riemannian manifold of zero dimensional isometry group which its Ricci curvature is positive (or maybe zero) somewhere?

I know that due to Joachim Lohkamp every smooth manifold of dimension at least $3$ admits a complete metric whose Ricci curvature is bounded between two negative constants.

Sorry if this question is belongs to MSE. I have no idea about it.

Question: Is there any Riemannian manifold of zero dimensional isometry group which its Ricci curvature is positive (or maybe zero) somewhere?

I know that due to Joachim Lohkamp every smooth manifold of dimension at least $3$ admits a complete metric whose Ricci curvature is bounded between two negative constants.

Sorry if this question is belongs to MSE. I have no idea about it.

Question: Is there any Riemannian manifold of zero dimensional isometry group which its Ricci curvature is positive (or maybe zero)?

I know that due to Joachim Lohkamp every smooth manifold of dimension at least $3$ admits a complete metric whose Ricci curvature is bounded between two negative constants.

Source Link
C.F.G
C.F.G
  • 4.2k
  • 6
  • 31
  • 65

Is there any Riemannian manifold of zero dimensional isometry group such that

Sorry if this question is belongs to MSE. I have no idea about it.

Question: Is there any Riemannian manifold of zero dimensional isometry group which its Ricci curvature is positive (or maybe zero) somewhere?

I know that due to Joachim Lohkamp every smooth manifold of dimension at least $3$ admits a complete metric whose Ricci curvature is bounded between two negative constants.