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Results tagged with riemannian-geometry
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user 36244
Riemannian Geometry is a subfield of Differential Geometry, which specifically studies "Riemannian Manifolds", manifolds with "Riemannian Metrics", which means that they are equipped with continuous inner products.
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Proof of a theorem of Jean-Pierre Serre on geodesics of closed Riemannian manifolds
An oft-cited theorem of Serre states that there are infinitely many geodesics between any two points in a closed Riemannian manifold. Could someone please provide an intuitive sketch of the proof?
- 135
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Some facts about cut-locus
Let $M$ be a 2-dimensional closed Riemmanian manifold diffeomorphic to $S^2$.
S.B.Myers says "the cut-locus of every point $x\in M$ is a finite tree."
How the set of point can be a tree? Wha …
- 135