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Results tagged with riemannian-geometry
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user 490280
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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Request for two unpublished articles of Detlef Gromoll
I am looking for two articles for my research purpose, which are entitled with "Convex riemannian manifolds" and "Convex sets in riemannian manifolds" by Detlef Gromoll.
I would appreciate it if anyon …
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Special property of flat spaces
I'm reading Eschenburg's paper Local convexity and nonnegative curvature — Gromov's proof of the sphere theorem recently. And I meet a little question. In 6.1 he said: let $M=\mathbb{R}^n$ be the eucl …
- 241
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Before focal point, the locally distance function is smooth
I'm reading Eschenburg's paper Local convexity and nonnegative curvature — Gromov's proof of the sphere theorem recently. And I meet a little question: In the proof of Lemma 7.4, He let $d$ be the sig …
- 241
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Detail in Perelman's proof of the soul conjecture
Referring to G. Perelman, Proof of the soul conjecture by Cheeger and Gromoll. Given a distance-nonincreasing retraction $P$ from an open complete manifold of nonnegative curvature onto its soul $S$, …
- 241
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Estimate the second derivative of a Jacobi field
I'm reading Local convexity and nonnegative curvature-Gromov's proof of the sphere theorem of Eschenburg recently. In his proof in Lemma 4.3, he consider the following question:
Suppose $0\leq K\leq k …
- 241
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A question on Cheeger-Colding theory
I'm reading Compactification of certain Kähler manifolds with nonnegative Ricci curvature by Gang Liu recently. And I feel hard to understand a statement in the paper. Now the assumption is $(M,g)$ is …
- 241
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Construct a hypersurface with fixed principal curvatures at a point
I'm reading Eschenburg's paper Local convexity and nonnegative curvature —
Gromov's proof of the sphere theorem recently. And I meet a little question: Given a point $p\in M$, $N\in T_pM$, we want to …
- 241