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**Sample text**

Consequently, if u : E —• (S,p2(u)dudu) is harmonic, then f ' o t c E - t (S,

However, the operator Tp is built up from the elliptic operator Da6x, for which we shall define a determinant following the lines of section 5. 2. The Faddeev-Popov determinant: the case G=H In this section, we assume that G = H so that Da9x = R\TX ° DR~X, where rx = De0x : TeG —* TXE. We remark that in this case, the assumption Hyp 3 can be replaced by the same assumption on the operator rx, namely: Hyp 3': The operator rz is a differential operator on S of order 1 with smooth coefficients which is injective and has an injective symbol.

4, be the harmonic map. Then =W'(j)eA<-i. 20) This is independent of the choice of g € 7t~1(^dz2). Namely, for g e M-i, any other g' € ir~1(ir(g)) is of the form