×
Tanno, Shukichi

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

Tohoku Math. J., II. Ser. 25, 391-403 (1973).
Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page
scan of Zbl 0266.53033

Cited in 1 Review
Cited in 30 Documents

MSC:

53C20 Global Riemannian geometry, including pinching
PDF BibTeX XML Cite
\textit{S. Tanno}, Tôhoku Math. J. (2) 25, 391--403 (1973; Zbl 0266.53033)
Full Text: DOI
  • logo of hbz
  • logo of WorldCat

References:

[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
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.