黎曼流形的抛物性与度量的共形形变  

Parabolicity and Conformal Deformations of the Metrics on a Riemannian Manifold

作　　者：张宗劳[1] 

机构地区：[1]西安交通大学理学院

出　　处：《西南师范大学学报（自然科学版）》2005年第1期34-36,共3页Journal of Southwest China Normal University(Natural Science Edition)

摘　　要：借助于黎曼流形的抛物性概念研究黎曼度量的共形形变问题, 证明了Gauss曲率小于某负常数的非紧完备2维黎曼流形其度量不可能共形形变到具有非负Gauss曲率的完备度量.Conformal deformations of the Metrics on a Riemannian manifold are investigated by using parabolicity, and it is proved that if a complete noncompact 2-dimensional Riemannian manifold has Gauss curvature less than a negative constant, its metric can not be conformally deformed to a complete metric with nonnegative Gauss curvature.

关 键 词：完备黎曼流形 抛物性 GAUSS曲率 共形形变 

分 类 号：O186.12[理学—数学]