Applications harmoniques, applications pluriharmoniques et existence de 2-formes parall�les non nulles

Abstract

Abstract. In this paper we study harmonic maps from a compact riemannian manifold equiped with a non trivial parallel 2-form, to a Kähler manifold of strongly negative curvature tensor or a riemannian manifold of strictly negative complex sectional curvature. In a first part we set up some rigidity results of Siu type. Then we obtain an upper bound for the rank of such maps in terms of the rank of the 2-form and deduce some vanishing theorems.Mathematics Subject Classification (1991). 58E20, 53C55, 53C20.

Harmonic maps and strictly pseudoconvex CR manifolds

“…Hence {(j)*R )£ and (</>*Pc)iy are nonpositive. As in Theorem 5.1, we obtain that if 0 is harmonic, d</>(£) = 0 and (^*PC)H = 0-Now, the end of the proof follows from the proof of Theorem 4.1 of [9]. □ A rigidity result for harmonic maps between Sasakian manifolds.…”

“…The assumptions on the curvature and on the rank of (p imply using a similar proof as in Theorem 4.1 of [9] that…”

Some properties of F-harmonic maps

“…Harmonic maps have been studied first by J. Eells and J.H.Sampson in the sixties and since then many works were done ( see [4], [9], [13], [16], [17], [21]) to cite a few of them. Extensions to notions of pharmonic, biharmonic, F -harmonic and f -harmonic maps were introduced and similar research has been carried out (see [1], [2], [3], [5], [12], [15], [18], [20]).…”

$$F$$ -harmonic maps as global maxima

“…Harmonic maps have been studied first by J. Eells and J.H.Sampson in the sixties and since then many articles have appeared ( see [6], [12], [16], [19], [20], [24]) to cite a few of them. Extensions to the notions of p-harmonic, biharmonic, F -harmonic and f -harmonic maps were introduced and similar research has been carried out (see [1], [2], [3], [7], [15], [18], [21], [23]).…”