Killing fields preserving totally geodesic, codimension-one foliations (Q1190677)

In the paper, there is studied the Lie algebra \(\mathfrak G\) of Killing vector fields preserving a codimension-one totally geodesic foliation \(\mathcal F\) on a complete Riemannian manifold \(M\). The foliation, which is induced on the universal covering of \(M\) is trivial and the induced metric has a simple form [\textit{R. A. Blumenthal} and \textit{J. J. Hebda}, Indiana Univ. Math. J. 33, 597-611 (1984; Zbl 0511.57021)]. Using this fact, the author determines bounds of the dimension of \(\mathfrak G\) and of the dimensions of some special subalgebras of \(\mathfrak G\) (such as, f.e., the subalgebra of Killing vector fields to \(\mathcal F\)).