Questions tagged [negative-curvature]
The negative-curvature tag has no usage guidance.
4
questions with no upvoted or accepted answers
10
votes
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answers
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views
Examples of quasi-negative but not negative holomorphic sectional curvature
Let $(X,\omega)$ be a compact Kähler manifold and call $\operatorname{HSC}_{\omega}(x,[v])$ the holomorphic sectional curvature of the Chern connection of $\omega$ at the point $x\in X$ in the ...
2
votes
0
answers
91
views
Locus maximizing the holomorphic sectional curvature in a non-compact Hermitian symmetric space
Is there a quick way to prove the following statement, if possible without resorting to the classification of simple Lie groups?
Let $G$ be a simple Lie group of non-compact Hermitian type of rank $r$...
1
vote
0
answers
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views
Maximal geodesically convex function interpolating three points on the hyperbolic plane
Crossposted on MSE: https://math.stackexchange.com/questions/4282998/maximal-geodesically-convex-function-interpolating-three-points-on-the-hyperboli
Let $M$ be a two-dimensional Hadamard manifold. ...
0
votes
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answers
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Bounding Riemannian Distance
If $(M,g)$ is a geodesically complete Riemannian manifold of negative sectional curvature bounded below by $K<0$ then is it true that for any $x,y,x_0\in M$
$$
d_H(
Log(x_0,x),Log(y,x_0)
)
\leq
d_M^...