具有不变伪度量的李群的Ricci曲率和数量曲率

THE RICCI CURVATURES AND THE SCALAR CURVATURES OF BI-INVARIANT PSEUDO-RIEMANNIAN METRICS ON LIE GROUPS

说明了具有不变伪度量的李群的Ｒｉｃｃｉ曲率和数量由率只与李群的李代数的结构有关，确定了Ｒｉｃｃｉ曲率严格正的李群，并给出了Ｒｉｃｃｉ曲率与数量曲率保持定号的一些充分条件．

In this paper we demonstrate that the Ricci curvatures and the scalar curvatures of the bi-invariant pseudo-Riemannian metrics on a Lie group G are determined by the Lie algebra structure of G. We also classified the Lie groups of strictly positive Ricci curvatures and give some sufficient conditions under which the Ricci curvatures and the scalar curvatures remain the fixed signs.