Sectional curvatures of manifolds of the Kaluza-Klein type (Q1387287)

The author studies sectional curvatures of Riemannian manifolds of Kaluza-Klein (KK)-type. [His definition of the notion ``KK-type'' differs from the definition of a ``generalized KK-model'' used, e.g., in \textit{V. R. Gavrilov}, \textit{U. Kasper}, \textit{V. N. Melnikov} and \textit{M. Rainer}, Gen. Relativ. Gravitation 31, No. 2, 139-155 (1999).] He defines a gyroscopic system and gives relations between both notions. The main result of the paper is a set of inequalities for the sectional curvature of KK-type manifolds. Some topological considerations follow, and the restriction to the three-dimensional case elucidates the result.