Eigenvalues of the Laplacian of Riemannian manifolds. (English) Zbl 0266.53033


53C20 Global Riemannian geometry, including pinching
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[1] M. BERGER, Le spectre des varietes riemanniennes, Rev. Roum. Math. Pure et Appl., 13(1969), 915-931. · Zbl 0181.49603
[2] M. BERGER, P. Gauduchon et E. Mazet, Le Spectre d’une Variete riemannienne, Lect Notes in Math. Springer-Verlag, 194.
[3] M. KAC, Can one hear the shape of a drum ? Amer. Math. Monthly, 73 (April, 1966), 1-23. · Zbl 0139.05603
[4] M. KURITA, On the holonomy group of the conformally flat Riemmannian manifold, Nagoya Math. J., 9(1955), 161-171. · Zbl 0066.16002
[5] M. MATSUMOTO, On Kahlerian spaces with parallel or vanishing Bochner curvature tensor, Tensor (N. S), 20 (1969), 25-28. · Zbl 0174.25001
[6] H. F. MCKEAN AND I. M. SINGER, Curvature and the eigenvalues of the Laplacian, J. Diff. Geometry, 1 (1967), 43-69. · Zbl 0198.44301
[7] J. MILNOR, Eigenvalues of the Laplace operator on certain manifolds, Proc. Nat. Sci U. S. A., 51(1964), 542. · Zbl 0124.31202
[8] M. OBATA, Certain conditions for a Riemannian manifold to be isometric with a sphere, J. Math. Soc. Japan, 14(1962), 333-340. · Zbl 0115.39302
[9] V. K. PATODI, Curvature and the eigenforms of the Laplace operator, J. Diff. Geometry, 5(1971), 233-249. · Zbl 0211.53901
[10] V. K. PATODI, Curvature and the fundamental solution of the heat operator, J. India Math. Soc., 34(1970), 269-285. · Zbl 0237.53039
[11] T. SAKAI, On eigenvalues of Laplacian and curvature of Riemannian manifold, Thok Math. J., 23(1971), 589-603. · Zbl 0237.53040
[12] H. TAKAGI AND Y. WATANABE, On the holonomy groups of Kahlerian manifolds wit vanishing Bochner curvature tensor, Thoku Math. J., · Zbl 0271.53031
[13] S. TANNO, Compact conformally flat Riemannian manifolds, to appear in J. Diff. Geometry, 8 (1973). · Zbl 0278.53033
[14] S. TANNO, Euler-Poincare characteristics and curvature tensors, Thoku Math. J., 2 (1973), 33-52. · Zbl 0263.53033
[15] S. TANNO, An inequality for 4-dimensional Kahlerian manifolds, Proc. Japan Acad., 4 (1973), 257-261. · Zbl 0273.53023
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