Einstein metrics and fibred Riemannian structures (Q790459)

Given a fiber space for which total space, fibers, and base spaces are Einstein and the fibers are totally geodesic. Let \(< , >\) be the metric in the total space and V, H denote the vertical and horizontal projection. Vary the metric by \(<X,Y>_ t=t<VX,VY>+<HX,HY>.\) The author proves that locally exactly one of these metrics is Einstein as long as \(2R_ F/R_ B\neq \dim F/\dim B\) (R curvature scalar, F fiber, B base). He shows that earlier examples of \textit{G. R. Jensen} [J. Differ. Geom. 8, 599-614 (1973; Zbl 0284.53038)] and \textit{W. Ziller} [Math. Ann. 259, 351- 358 (1982; Zbl 0469.53043)] are special cases of his construction.