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Search: All articles in the CMB digital archive with keyword geodesic

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1. CMB 2013 (vol 57 pp. 870)

Parlier, Hugo
A Short Note on Short Pants
It is a theorem of Bers that any closed hyperbolic surface admits a pants decomposition consisting of curves of bounded length where the bound only depends on the topology of the surface. The question of the quantification of the optimal constants has been well studied and the best upper bounds to date are linear in genus, a theorem of Buser and Seppälä. The goal of this note is to give a short proof of a linear upper bound which slightly improve the best known bound.

Keywords:hyperbolic surfaces, geodesics, pants decompositions
Categories:30F10, 32G15, 53C22

2. CMB 2012 (vol 57 pp. 209)

Zhao, Wei
Erratum to the Paper "A Lower Bound for the Length of Closed Geodesics on a Finsler Manifold"
We correct two clerical errors made in the paper "A Lower Bound for the Length of Closed Geodesics on a Finsler Manifold".

Keywords:Finsler manifold, closed geodesic, injective radius
Categories:53B40, 53C22

3. CMB 2012 (vol 57 pp. 194)

Zhao, Wei
A Lower Bound for the Length of Closed Geodesics on a Finsler Manifold
In this paper, we obtain a lower bound for the length of closed geodesics on an arbitrary closed Finsler manifold.

Keywords:Finsler manifold, closed geodesic, injective radius
Categories:53B40, 53C22

4. CMB 2011 (vol 55 pp. 870)

Wang, Hui; Deng, Shaoqiang
Left Invariant Einstein-Randers Metrics on Compact Lie Groups
In this paper we study left invariant Einstein-Randers metrics on compact Lie groups. First, we give a method to construct left invariant non-Riemannian Einstein-Randers metrics on a compact Lie group, using the Zermelo navigation data. Then we prove that this gives a complete classification of left invariant Einstein-Randers metrics on compact simple Lie groups with the underlying Riemannian metric naturally reductive. Further, we completely determine the identity component of the group of isometries for this type of metrics on simple groups. Finally, we study some geometric properties of such metrics. In particular, we give the formulae of geodesics and flag curvature of such metrics.

Keywords:Einstein-Randers metric, compact Lie groups, geodesic, flag curvature
Categories:17B20, 22E46, 53C12

5. CMB 2011 (vol 54 pp. 396)

Cho, Jong Taek; Inoguchi, Jun-ichi; Lee, Ji-Eun
Parabolic Geodesics in Sasakian $3$-Manifolds
We give explicit parametrizations for all parabolic geodesics in 3-dimensional Sasakian space forms.

Keywords:parabolic geodesics, pseudo-Hermitian geometry, Sasakian manifolds
Category:58E20

6. CMB 2005 (vol 48 pp. 340)

Andruchow, Esteban
Short Geodesics of Unitaries in the $L^2$ Metric
Let $\M$ be a type II$_1$ von Neumann algebra, $\tau$ a trace in $\M$, and $\l2$ the GNS Hilbert space of $\tau$. We regard the unitary group $U_\M$ as a subset of $\l2$ and characterize the shortest smooth curves joining two fixed unitaries in the $L^2$ metric. As a consequence of this we obtain that $U_\M$, though a complete (metric) topological group, is not an embedded riemannian submanifold of $\l2$

Keywords:unitary group, short geodesics, infinite dimensional riemannian manifolds.
Categories:46L51, 58B10, 58B25

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