Curvatures of Tangent Bundles with Cheeger-Gromoll Metric

Abstract

Although the Sasaki metric For example, O. Kowalski has shown that it is never locally symmetric unless the base metric is locally Euclidean. E. Musso and F. Tricerri [6] have generalized this.fact. They have shown that it has a constant scalar curvature if and only if the base metric is flat.