The BFK-gluing formula and the curvature tensors on a 2-dimensional compact hypersurface
| Autor: | Yoonweon Lee, Klaus Kirsten |
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| Rok vydání: | 2020 |
| Předmět: |
Mathematics - Differential Geometry
High Energy Physics - Theory Pure mathematics Polynomial Trace (linear algebra) Operator (physics) Scalar (mathematics) FOS: Physical sciences Statistical and Nonlinear Physics Mathematical Physics (math-ph) Curvature Manifold 58J20 Mathematics - Spectral Theory Hypersurface Differential Geometry (math.DG) High Energy Physics - Theory (hep-th) Principal curvature FOS: Mathematics Mathematics::Differential Geometry Geometry and Topology Spectral Theory (math.SP) Mathematical Physics Mathematics |
| Zdroj: | Journal of Spectral Theory. 10:1007-1051 |
| ISSN: | 1664-039X |
| DOI: | 10.4171/jst/320 |
| Popis: | In the proof of the BFK-gluing formula for zeta-determinants of Laplacians there appears a real polynomial whose constant term is an important ingredient in the gluing formula. This polynomial is determined by geometric data on an arbitrarily small collar neighborhood of a cutting hypersurface. In this paper we express the coefficients of this polynomial in terms of the scalar and principal curvatures of the cutting hypersurface embedded in the manifold when this hypersurface is 2-dimensional. Similarly, we express some coefficients of the heat trace asymptotics of the Dirichlet-to-Neumann operator in terms of the scalar and principal curvatures of the cutting hypersurface. 28 pages |
| Databáze: | OpenAIRE |
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