On focal stability in dimension two

On focal stability in dimension two

In Kupka et al. 2006 appears the Focal Stability Conjecture: the focal decomposition of the generic Riemann structure on a manifold M is stable under perturbations of the Riemann structure. In this paper, we prove the conjecture when M has dimension two, and there are no conjugate points.

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Veröffentlicht in:Anais da Academia Brasileira de Ciências 2007-03, Vol.79 (1), p.1-11
Hauptverfasser: Peixoto, Mauricio M, Pugh, Charles C
Format: Artikel
Sprache:eng
Schlagworte:
decomposição focal
espaço de Teichmuller
estabilidade focal
focal decomposition
focal stability
genericity
genetricidade
geodesics
geodésicas
MULTIDISCIPLINARY SCIENCES
Teichmuller space
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Zusammenfassung:In Kupka et al. 2006 appears the Focal Stability Conjecture: the focal decomposition of the generic Riemann structure on a manifold M is stable under perturbations of the Riemann structure. In this paper, we prove the conjecture when M has dimension two, and there are no conjugate points.
ISSN:0001-3765
1678-2690
0001-3765
1678-2690
DOI:10.1590/S0001-37652007000100001