\(\lambda\)-automorphisms of a Riemannian foliation
The notion of \(\lambda\)-automorphisms \((\lambda \in \mathbb{R})\) of a Riemannian foliation \(\mathcal F\) on a manifold \(M\) was introduced first by \textit{F. W. Kamber, Ph. Tondeur} and \textit{G. Toth} in the paper ``Transversal Jacobi fields for harmonic foliations'' [Mich. Math. J. 34, 261-266 (1987; Zbl 0629.53031)]. Briefly speaking, such \(\lambda\)- automorphisms are sections \(s\) of the normal bundle \(Q = TM/T{\mathcal F}\) which satisfy a particular differential equation involving \(\lambda\), the Laplace operator in \(Q\), the transverse Levi-Civita connection, the transverse divergence, etc. Here, several identities for \(\lambda\)- automorphisms are derived. Also, some geometrical conditions sufficient for a \(\lambda\)-automorphism \(s\) to be either transversely Killing or transversely conformal are given.
scientific article; zbMATH DE number 792879