Essential Conformal Fields in Pseudo-Riemannian Geometry. II

Journal of Mathematical Sciences

Kühnel, W.¹  Rademacher, H.-B.¹ 

关键词: conformal compactification;    projective quadric;    sphere inversion;    conformal group;    conformally closed;    null cone at infinity;   

DOI  :  

学科分类：数学（综合）

来源: University of Tokyo * Department of Mathematical Sciences

【 摘 要 】

Westudyconformalvectorfieldsonpseudo-Riemannianmanifolds.Inthecaseofconformallyflatmanifolds,themaintoolistheconformaldevelopmentmapintotheprojectivequadric.Ontheotherhand,weshowthatthereexistsapseudo-Riemannianmanifoldcarryingacompleteandessentialvectorfieldwhichisnotconformallyflat.Theexampleimpliesthatthereisnofinitedimensionalmodulispaceforsuchmanifolds.Therefore,apseudo-RiemanniananalogueofAlekseevskii'stheoremontheclassificationofessentialconformalvectorfieldscannotbeexpected.

【 授权许可】

Unknown