Rigidity of Complete Riemannian Manifolds without Conjugate Points

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.

Produktdetails

• Autoren: Patrick Emmerich
• Verlag: Shaker Verlag
• Sprache: Englisch
• Produktform: Taschenbuch
• Erschienen: 30.04.2015
• Seiten: 81
• Abmessung: 149 mm x 213 mm x 9 mm
• Gewicht: 137 g
• Serien: Berichte aus der Mathematik; Berichte aus der Mathematik
• Thema: Naturwissenschaften, Medizin, Informatik, Technik > Mathematik > Geometrie