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Atiyah, Michael; Bott, Raoul; Patodi, V. K.

On the heat equation and the index theorem. (English) Zbl 0257.58008

Invent. Math. 19, 279-330 (1973).
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Cited in 7 Reviews
Cited in 219 Documents

MSC:

58J20 Index theory and related fixed-point theorems on manifolds
35K05 Heat equation
53C20 Global Riemannian geometry, including pinching
53C55 Global differential geometry of Hermitian and Kählerian manifolds
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\textit{M. Atiyah} et al., Invent. Math. 19, 279--330 (1973; Zbl 0257.58008)
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References:

[1] Atiyah, M.F., Singer, I.M.: The index of elliptic operators, I. Ann. of Math.87, 484-530 (1968). · Zbl 0164.24001 · doi:10.2307/1970715
[2] Atiyah, M.F., Singer, I.M.; The index of elliptic operators, III. Ann. of Math.87, 546-604 (1968). · Zbl 0164.24301 · doi:10.2307/1970717
[3] Atiyah, M.F., Singer, I.M.: The index of elliptic operators, IV. Ann. of Math.93, 119-138 (1971). · Zbl 0212.28603 · doi:10.2307/1970756
[4] Atiyah, M.F., Singer, I.M.: The index of elliptic operators, V. Ann. of Math.93, 139-149 (1971). · Zbl 0212.28603 · doi:10.2307/1970757
[5] Atiyah, M.F., Singer, I.M.: The index of elliptic operators on compact manifolds. Bull. Amer. Math. Soc.69, 422-433 (1963). · Zbl 0118.31203 · doi:10.1090/S0002-9904-1963-10957-X
[6] Atiyah, M.F., Bott, R.: A Lefschetz fixed point formula for elliptic complexes, I. Ann. of Math.86, 374-407 (1967). · Zbl 0161.43201 · doi:10.2307/1970694
[7] Atiyah, M.F., Bott, R.: A Lefschetz fixed point formula for elliptic complexes, II. Ann. of Math.88, 451-491 (1968). · Zbl 0167.21703 · doi:10.2307/1970721
[8] Atiyah, M.F., Bott, R., Shapiro, A.: Clifford modules. Topology3, Suppl. 1, 3-38 (1964).
[9] Atiyah, M.F., Hirzebruch, F.: Spin-manifolds and group actions. Essays on Topology and related topics dedicated to G. de Rham. Berlin-Heidelberg-New York: Springer 1970. · Zbl 0193.52401
[10] Berger, M.: Le spectre d’une variété riemannienne. Lecture Notes in Mathematics194. Berlin-Heidelberg-New York: Springer 1971.
[11] Bott, R.: Vector fields and characteristic numbers. Mich. Math. J.14, 231-244 (1967). · Zbl 0145.43801 · doi:10.1307/mmj/1028999721
[12] Bott, R.: The periodicity theorem for the classical groups and some of its applications. Advances in Math.4, 353-411 (1970). · Zbl 0231.55010 · doi:10.1016/0001-8708(70)90030-7
[13] Eisenhart, L.: Introduction to Differential Geometry. Princeton: University Press 1940. · Zbl 0026.35001
[14] Gel’fand, I.M.: The cohomology of some infinite-dimensional Lie algebras. Proceedings of International Congress, Nice,I, 95-110 (1970).
[15] Gilkey, P.: Curvature and the eigenvalues of the Laplacian for elliptic complexes. Advances in Mathematics (to appear). · Zbl 0259.58010
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[17] Hitchin, N.: Harmonic Spinors (to appear). · Zbl 0284.58016
[18] McKean, H. P., Jr., Singer, I. M.: Curvature and the eigenvalues of the Laplacian. J. Differential Geometry1, 43-69 (1967). · Zbl 0198.44301
[19] Minakshisundaram, S., Pleijel, A.: Some properties of the eigenfunctions of the Laplace operator on Riemannian manifolds. Canadian J. Math.1, 242-256 (1949). · Zbl 0041.42701 · doi:10.4153/CJM-1949-021-5
[20] Palais, R.: Seminar on the Atiyah-Singer Index Theorem. Ann. of Math. Studies57, Princeton, 1965. · Zbl 0137.17002
[21] Patodi, V.K.: Curvature and the eigenforms of the Laplace operator. J. Diff. Geometry5, 233-249 (1971). · Zbl 0211.53901
[22] Patodi, V.K.: An analytic proof of Riemann-Roch-Hirzebruch theorem for Kaehler manifolds. J. Diff. Geometry5, 251-283 (1971). · Zbl 0219.53054
[23] Seeley, R.T.: Complex powers of an elliptic operator. Proc. Sympos. Pure Math.10, Amer. Math. Soc. 288-307, 1967. · Zbl 0159.15504
[24] Weyl, H.: The classical groups, Princeton University Press, Princeton, 1946. · Zbl 1024.20502
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