Emmerich, P: Rigidity of Complete Riemannian Manifolds witho
(Sprache: Englisch)
A complete Riemannian manifold is without conjugate points if every geodesic in its universal Riemannian covering is length-minimizing. Riemannian 2-tori without conjugate points are flat by a theorem of Eberhard Hopf from 1948. The present thesis contains...
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A complete Riemannian manifold is without conjugate points if every geodesic in its universal Riemannian covering is length-minimizing. Riemannian 2-tori without conjugate points are flat by a theorem of Eberhard Hopf from 1948. The present thesis contains rigidity results for complete Riemannian metrics without conjugate points on the plane and on the 2-cylinder. In these cases the area growth of the metric is a particularly natural condition and leads to optimal results. The thesis further contains rigidity results for the case of conformally flat cylinders of dimension three and greater.
Bibliographische Angaben
- Autor: Patrick Emmerich
- 81 Seiten, Maße: 14,9 x 21,3 cm, Kartoniert (TB), Englisch
- Verlag: Shaker
- ISBN-10: 3844023232
- ISBN-13: 9783844023237
- Erscheinungsdatum: 07.11.2013
Sprache:
Englisch
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