Abstract. Let $(M,g)$ be a pseudo--Riemannian manifold and $(TM,g^C)$ its tangent bundle equipped with the complete lift metric $g^C$. Using the notion of a harmonic almost product structure on $(TM,g^C)$, as introduced in , we define and study harmonic connections. This notion is used to introduce harmonic tensor fields of type $(1,2)$. We illustrate the theory by treating harmonic Ambrose--Singer, almost symplectic, almost complex and almost product connections, harmonic foliations and minimal plane fields. Finally, we construct examples on $TM$ by means of the lifting procedure.
AMS Subject Classification
harmonic tensor fields
Received July 15, 1996. (Registered under 6137/2009.)