References
Atiyah M, Bott R and Patodi V K 1973 On the heat equation and the index theorem;Invent. Math. 19 279–330
Chern S 1944 A simple intrinsic proof of the Gauss-Bonnet formula for closed Riemannian manifolds;Ann. Math. 45 747–752
Gilkey P 1972Curvature and the eigenvalues of the Laplacian for geometrical elliptic complex, Thesis, Harvard University
Gilkey P 1973 Curvature and the eigenvalues of the Laplacian for elliptic complexes;Adv. Math. 10 344–382
Gilkey P 1975a The spectral geometry of a Riemannian manifold;J. Diff. Geo. 10 601–618
Gilkey P 1975b Local invariants of a pseudo-Riemannian manifold;Math. Scand. 36 109–130
Gilkey P 1979 Recursion relations and the asymptotic behaviour of the eigenvalues of the Laplacian;Compositio Mathematica 38 201
McKean H P and Singer I M 1967 Curvature and the eigenvalues of the Laplacian;J. Diff. Geo. 1 43–69
Patodi V K 1970 Curvature and the fundamental solution of the heat equation;J. Indian Math. Soc. 34 269–285
Patodi V K 1971 Curvature and the eigenforms of the Laplace operator;J. Diff. Geo. 5 233–249
Sakai T 1971 On the eigenvalues of the Laplacian and curvature of Riemannian manifoldTohuku Math. J. 23 589–603
Weyl H 1946The classical groups (Princeton: University Press)
Author information
Authors and Affiliations
Additional information
Research partially supported by NSF grant MCS76-23465 and by Sloan Foundation Grant BR-1687.
Rights and permissions
About this article
Cite this article
Gilkey, P.B. Curvature and the heat equation for the de Rham complex. Proc Math Sci 90, 47–79 (1981). https://doi.org/10.1007/BF02867017
Issue Date:
DOI: https://doi.org/10.1007/BF02867017