Global theory of geodesically equivalent metrics

• Applicant: Professor Dr. Vladimir Matveev
• Subject Area: Mathematics
• Term: from 2003 to 2011
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 5407287

Two Riemannian metrics g and g on one manifold Mn are called geodesically equivalent, if every geodesic of g, considered as an unparameterized curve, is a geodesic of g. An autodiffeomorphism of a Riemannian manifold is called a projective transformation, if it takes (unparameterized) geodesics to geodesics. My aim is to - solve the Beltrami Problem for closed 3-manifolds ... - prove the Projective Lichnerowicz-Obata-Solodovnikov Conjecture ... - and to prove the Geodesic Rigidity Problem ...

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