Levi harmonic maps of contact Riemannian manifolds
The authors introduce the notion of a \textit{Levi harmonic map} \(f:M\rightarrow M'\) from an almost contact semi-Riemannian manifold \(M\) into a semi-Riemannian manifold \(M'\) and study the Levi harmonicity for CR maps between two almost contact semi-Riemannian manifolds. The paper also discusses several ramifications of the theory of harmonic morphisms, within contact Riemannian geometry, such as Levi harmonic and pseudoharmonic morphisms. In particular it is shown that any Levi harmonic morphism \(f:M\rightarrow M'\) of an almost contact Riemannian manifold \(M\) into a Riemannian manifold \(M'\) is a Levi harmonic map and a similar result for pseudoharmonic morphisms holds only for Sasakian target manifolds \(M\). The work is enriched with many interesting examples.
scientific article; zbMATH DE number 6370422
scientific article