Curvature and the heat equation for the de Rham complex

DOI10.1007/BF02867017zbMath0481.58027MaRDI QIDQ1162297

Peter B. Gilkey

Publication date: 1981

Published in: Proceedings of the Indian Academy of Sciences. Mathematical Sciences (Search for Journal in Brave)

zbMATH Keywords

Chern-Gauss-Bonnet theoremEuler formheat equation methodsEuler-Poincare characteristiccompact Riemannian manifold without boundarycovariant derivatives of the curvature tensorLaplacian on p- forms

Mathematics Subject Classification ID

Spectral problems; spectral geometry; scattering theory on manifolds (58J50) de Rham theory in global analysis (58A12) Global Riemannian geometry, including pinching (53C20) Heat and other parabolic equation methods for PDEs on manifolds (58J35)

Related Items (2)

Universal curvature identities ⋮ Dimensional curvature identities on pseudo-Riemannian geometry

Cites Work

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• The spectral geometry of a Riemannian manifold
• Curvature and the eigenvalues of the Laplacian
• Curvature and the eigenforms of the Laplace operator
• On eigen-values of Laplacian and curvature of Riemannian manifold
• On the heat equation and the index theorem
• Curvature and the eigenvalues of the Laplacian for elliptic complexes
• A simple intrinsic proof of the Gauss-Bonnet formula for closed Riemannian manifolds
• Local invariants of a pseudo-Riemannian manifold.

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