Weakly symmetric spaces in complex and quaternionic space forms

摘要

In Riemannian geometry a homogeneous Riemannian manifold is one of the most interesting and important objects. The category of homogeneous Riemannian manifolds includes the following three important subcategories: the category of naturally reductive Riemannian homogeneous spaces, the category of weakly symmetric spaces (which is introduced by A. Selberg [14]) and the category of Riemannian symmetric spaces. The last category is contained in the former two. But very few non-symmetric examples are known in the category of weakly symmetric spaces.