ACTA issues

Harmonic connections

Eduardo García--Río, Lieven Vanhecke, M. Elena Vázquez--Abal$^*$

Acta Sci. Math. (Szeged) 62:3-4(1997), 583-607

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 [11], 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 (1991): 53C05

Keyword(s): Tangent bundles, endomorphism fields, harmonic maps, harmonic connections, harmonic tensor fields

Received July 15, 1996. (Registered under 6137/2009.)