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A Note on the Fundamental Solution of the Heat Operator on Forms
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An approximate solution of the heat equation on p-forms on an n-dimensional manifold is constructed. This is used to create a fundamental solution of the heat operator. It is shown there is a link between this solution and the generalized Gauss-Bonnet theorem on manifolds.
Abstract
An approximate solution of the heat equation on p-forms on an n-dimensional manifold is constructed. This is used to create a fundamental solution of the heat operator. It is shown there is a link between this solution and the generalized Gauss-Bonnet theorem on manifolds.
참고문헌 (5)
- S. Minakshisundaram, "Some properties of the eigenfunctions of the Laplace operator on Riemannian manifolds", Canad. J. Math, 1, pp.242~256 (1949)
- V. K. Patodi, "Curvature and the Eigenforms of the Laplace Operator", J. Diff. Geom, 5, pp.233~249 (1971)
- H. P. McKean, "Curvature and the eigenvalues of the Laplacian", J. Diff. Geom, 1, pp.43~69 (1967)
- S. Goldberg, "Curvature and Homology" (1970), Dover
- S. S. Chern, "Lecture Notes in Differential Geometry" (1999), World Sceientific
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