Global theory of geodesically equivalent metrics

测地等效度量的全局理论

• 批准号: 5407287
• 负责人: Professor Dr. Vladimir Matveev
• 金额: --
• 依托单位: Lehrstuhl für Differentialgeometrie
• 依托单位国家: 德国
• 项目类别: Priority Programmes
• 财政年份: 2003
• 资助国家: 德国
• 起止时间: 2002-12-31 至 2010-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/5407287?language=en
• 关键词: Global; theory; geodesically; equivalent; metrics

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 ...

称流形Mn上的两个黎曼度量g和g是测地线等价的，如果g的每一条测地线都是g的测地线，且g是一条非参数曲线.黎曼流形的自同构称为射影变换，如果它将（非参数化的）测地线化为测地线。我的目标是-解决封闭三维流形的贝尔特拉米问题. - 投影Lichnerowicz-Obata-Solodovnikov猜想- 为了证明测地线刚性问题