Differential equations and their general solutions, as well as nonexistence theorems for six invariant classes of the vacuum constraint equations
摘要
Abstract
In this paper, we classify the vacuum constraint equations of General Relativity using the representation theory of classical groups. We also provide general solutions for the differential equations of each class and prove vanishing (nonexistence) theorems for these solutions using the Bochner technique, which is an important tool in Geometric Analysis.