一类新的伪黎曼可解代数里奇孤立子

A New Class of Pseudo-Riemannian Solvable Algebraic Ricci Solitons

里奇孤立子是一类重要的黎曼度量,它是一类重要的哈密尔顿曲率流的解,有重要的几何性质,具有重要的理论研究价值。在本文中,我们研究了在可解连通李群上构造伪黎曼代数里奇孤立子的一般方法,并在可解李群上构造了伪黎曼代数里奇孤立子,给出了它们等距的充分必要条件。

Ricci soliton is an important Riemannian metric, which is an important solution of the Hamilton curvature flow. So Ricci soliton has important geometry properties and significant research values. In this paper, we study the generally method of constructing pseudo Riemannian algebraic soliton on solvable connected Lie group, and we get the pseudo Riemannian algebraic soliton. Besides, we give the sufficient and necessary conditions in which two pseudo Riemannian algebraic soliton are isometrical to each other.