- #1
Sajet
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Sorry if this question seems too trivial for this forum.
A grad student at my university told me that a compact Riemannian manifold always has lower and upper curvature bounds.
Is this really true? The problem seems to be that I don't fully understand the curvature tensor's continuity etc.
What makes me a little skeptical is that I already spent quite a lot of time trying to find a source where this is explicitly stated, without any success. Usually I would expect such a statement as basic as this to appear in lots of books or lecture notes.
A grad student at my university told me that a compact Riemannian manifold always has lower and upper curvature bounds.
Is this really true? The problem seems to be that I don't fully understand the curvature tensor's continuity etc.
What makes me a little skeptical is that I already spent quite a lot of time trying to find a source where this is explicitly stated, without any success. Usually I would expect such a statement as basic as this to appear in lots of books or lecture notes.