The heat kernel for deformed spheres

Abstract

We derive the asymptotic expansion of the heat kernel for a Laplace operator acting on deformed spheres. We calculate the coefficients of the heat kernel expansion on two- and three-dimensional deformed spheres as functions of deformation parameters. We find that under some deformation the conformal anomaly for free scalar fields on $R^4\times {\tilde{S}}^2$ and $R^6\times {\tilde{S}}^2$ is canceled.

10 pages, latex, no figures

References in corpus (5)

• Vacuum energy on orbifold factors of spheres
• Conformal anomalies on Einstein spaces with Boundary
• Finite-Temperature Scalar Field Theory in Static de Sitter Space
• Functional determinants on regions of the plane and sphere
• The trace of the heat kernel on a compact hyperbolic 3-orbifold

Cited by in corpus (5)

• Heat kernel expansion: user's manual
• Effective actions on the squashed three-sphere
• Spectral analysis and zeta determinant on the deformed spheres
• A Conformally Invariant Holographic Two-Point Function on the Berger Sphere
• Casimir energy for the scalar field: a global approach with cut-off exponential function