Generalized Gradients and Asymptotics of the Functional Trace

Thomas P. Branson and Bent Ørsted
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Thomas P. Branson: The University of Iowa, Department of Mathematics
Bent Ørsted: The University of Iowa, Department of Mathematics

A chapter in Deformations of Mathematical Structures, 1989, pp 247-262 from Springer

Abstract: Abstract Let G be a generalized gradient on a compact, Riemannian n-manifold M, carrying an 0(n)-irreducible tensor bundle F to another such bundle E, and suppose that G*G is elliptic but not conformally covariant. Let Tr0 denote the trace of the compression to the Hodge sector R(G) in the decomposition L2(E) = R(G) ⊕N(G*). Then if ω∈C∞(M), Tt0 ω exp(-t G G*) has a small-time asymptotic expansion in powers of t, plus a log t term in the case of even n. All coefficients except that of t0 are integrals of local expressions. For G = d: C∞(M) → C∞(Λ1(M)) and n = 4, the coefficient of log t is nonzero for some ω whenever the scalar curvature is not constant.

Keywords: Riemannian Manifold; Scalar Curvature; Heat Kernel; Generalize Gradient; Conformal Variation (search for similar items in EconPapers)
Date: 1989
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-94-009-2643-1_23

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DOI: 10.1007/978-94-009-2643-1_23

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