Equivariant heat invariants of the Laplacian and nonmininmal operators on differential forms
نویسنده
چکیده
In this paper, we compute the first two equivariant heat kernel coefficients of the Bochner Laplacian on differential forms. The first two equivariant heat kernel coefficients of the Bochner Laplacian with torsion are also given. We also study the equivariant heat kernel coefficients of nonmininmal operators on differential forms and get the equivariant Gilkey-Branson-Fulling formula. MSC: 58J05,54A14
منابع مشابه
Heat Kernel Asymptotics for Laplace Type Operators and Matrix Kdv Hierarchy
We study the heat kernel asymptotics for the Laplace type differential operators on vector bundles over Riemannian manifolds. In particular this includes the case of the Laplacians acting on differential p-forms. We extend our results obtained earlier for the scalar Laplacian and present closed formulas for all heat invariants associated with these operators. As another application, we present ...
متن کاملEquivariant Moving Frames for Euclidean Surfaces
The purpose of this note is to explain how to use the equivariant method of moving frames, [1, 10], to derive the differential invariants, invariant differential operators and invariant differential forms for surfaces in three-dimensional Euclidean space. This is, of course, a very classical problem and the results are not new; for the classical moving frame derivation, see, for instance, [2, 3...
متن کاملEquivariant Spectral Flow and a Lefschetz Theorem on Odd Dimensional Spin Manifolds
As one of the most important theories in mathematics, Atiyah-Singer index theorems have various profound applications and consequences. At the same time, there are several ways to prove these theorems. Of particular interest is the heat kernel proof, which allows one to obtain refinements of the index theorems, i.e., the local index theorems for Dirac operators. Readers are referred to [BGV] fo...
متن کاملWeighted composition operators on measurable differential form spaces
In this paper, we consider weighted composition operators betweenmeasurable differential forms and then some classic properties of these operators are characterized.
متن کاملTHE LAPLACIAN ON p-FORMS ON THE HEISENBERG GROUP
The Novikov-Shubin invariants for a non-compact Riemannian manifold M can be defined in terms of the large time decay of the heat operator of the Laplacian on L p-forms, △p, on M . For the (2n + 1)-dimensional Heisenberg group H2n+1, the Laplacian △p can be decomposed into operators△p,n(k) in unitary representations β̄k which, when restricted to the centre of H, are characters (mapping ω to exp(...
متن کامل