Harmonic spaces in Riemannian geometry

• Applicant: Professor Dr. Gerhard Knieper
• Subject Area: Mathematics
• Term: from 2003 to 2006
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 5407214

Riemannian geometry aims at a general understanding of curved spaces, local curvature properties, global properties such as topology or symmetries, and their interrelation. Harmonic Riemannian spaces are characterized by a strong isotropy property, namely by constant mean curvature of their distance spheres. ... This research project aims at structure or classification results for noncompact harmonic spaces, possibly under suitable additional geometric assumptions, e.g. nonpositive curvature, compact quotients or homogeneity. For the investigations, differential geometry, dynamical and algebraic methods shall be combined into Euclidean (or Hilbert) spaces, asymptotic geometry, the geodesic flow, structure theory of homogeneous Einstein spaces.

• DFG Programme: Priority Programmes
• Subproject of: SPP 1154: Global Differential Geometry