Spektrale Geometrie und Huygenssches Prinzip für Tensorfelder und Differentialformen. II (Q1063920)

[For part I, cf. the first author, ibid. 1, No.2, 71-95 (1982; Zbl 0523.58042).] Let M be a closed Riemannian manifold of dimension n, let \(L=\epsilon \delta d+d\delta\) be a canonical Laplace operator which acts on differential forms of degree p. The structure of spectral invariant \(U_ 2(M)\) for the operator L is investigated. This invariant is the linear combination of the value \(\| R\|^ 2\), \(\| S\|^ 2\) and \(\| Weyl\|^ 2\) which are connected with geometric properties of the manifold M. The authors give explicit formula for the coefficients \(P_ i(n,p)\) of this linear combination. The analogous results are stated for the operators of a form \(L=\Delta\) or \(L=\Delta ((n-2)/4(n- 1))RI.\) For these operators all pairs (n,p) are computed for which \(P_ i(n,p)=0\), \(i=1,2,3\).