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.

Product details

• Authors: Patrick Emmerich
• Publisher: Shaker Verlag
• Languages: English
• Product format: Paperback / Softback
• Released: 30.04.2015
• No. of pages: 81
• Dimensions: 149 mm x 213 mm x 9 mm
• Weight: 137 g
• Series: Berichte aus der Mathematik; Berichte aus der Mathematik
• Subject: Natural sciences, medicine, IT, technology > Mathematics > Geometry