×
Tanno, Shukichi

Euler-Poincaré characteristics and curvature tensors. (English) Zbl 0263.53033

Tohoku Math. J., II. Ser. 25, 33-51 (1973).
Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page
scan of Zbl 0263.53033

Cited in 3 Documents

MSC:

53C20 Global Riemannian geometry, including pinching
53A45 Differential geometric aspects in vector and tensor analysis
Cite Review PDF
Full Text: DOI

References:

[1] C. B. ALLENDOERFER, Rigidity for spaces of class greater than one, Amer. Journ. Math., 61 (1939), 633-644. Zentralblatt MATH: JSTOR: links.jstor.org · Zbl 0021.15803 · doi:10.2307/2371317
[2] A. AVEZ, Applications de la formule de Gauss-Bonnet-Chern aux varietes a quatre dimen sions, C. R. Acad. Sci. Paris, 256 (1963), 5488-5490. · Zbl 0139.39301
[3] A. AVEZ, Characteristic classes and Weyl tensor: Applications to general relativity, Proc. Nat. Acad. Sci., 6 (1970), 265-268. JSTOR: · Zbl 0197.26503 · doi:10.1073/pnas.66.2.265
[4] M. BERGER, Sur les varietes a operateur de courbure positif, C. R. Acad. Sci. Paris, 253 (1961), 2832-2834. · Zbl 0196.54402
[5] M. BERGER, Sur les varietes dinstein compactes, C. R. IP Reunion de Gr. Math dxp. Latine, Louvain-Belgique (1966), 35-55. · Zbl 0178.56001
[6] M. BERGER, Le spectre des varietes riemanniennes. Rev. Roum. Math. Pures et Appl., 13 (1968), 915-931. · Zbl 0181.49603
[7] M. BERGER, P. Gauduchon and E. Mazet, Le Spectre d’une variete riemannienne, Lee Notes in Math. No. 194, Springer-Verlag. · Zbl 0223.53034
[8] R. L. BISHOP AND S. I. GOLDBERG, Some implications of the generalized Gauss-Bonne theorem, Trans. Amer. Math. Soc, 112 (1964), 508-535. JSTOR: · Zbl 0133.15101 · doi:10.2307/1994158
[9] S. BOCHNER, Vector fields and Ricci curvature, Bull. Amer. Math. Soc, 52 (1946), 776 797. · Zbl 0060.38301 · doi:10.1090/S0002-9904-1946-08647-4
[10] S. BOCHNER, Curvature and Betti numbers, Ann. of Math., 49 (1948), 379-390 JSTOR: · Zbl 0038.34401 · doi:10.2307/1969287
[11] E. CARTAN, Sur la possibilite de plonger un espace riemannien donne dans un espac euclidien, Ann. de Soc. Polon. Math., 6 (1927), 1-7. · JFM 54.0763.05
[12] D. GROMOLL, W. Klingenberg, and W. Meyer, Riemannsche Geometrie im Groen, Lee Notes in Math. No. 55, Springer-Verlag. · Zbl 0293.53001 · doi:10.1007/BFb0079185
[13] M. JANET, Sur la possibilite de plonger un espace riemannien donne dans espace euclidien, Ann.de Soc. Polon. Math., 5, (1926), 38-43. · JFM 53.0699.01
[14] W. KLINGENBERG, ber Riemannsche Mannigfaltigkeiten mit nach oben beschrankte Krummung, Ann. Mat. Pura Appl., 60 (1962), 49-59. · Zbl 0112.13603 · doi:10.1007/BF02412764
[15] S. KOBAYASHI AND K. NOMIZU, Foundations of Differential Geometry, Vol. I, II, Intersci Publ., 1963, 1969. · Zbl 0119.37502
[16] D. MEYER, Sur les varietes riemanniennes a operateur de courbure positif, C. R. Acad Sci.Paris, 272 (1971), 482-485. · Zbl 0209.25301
[17] S. B. MYERS, Riemannian manifolds with positive mean curvature, Duke Math. Journ., 8 (1941), 401-404. Zentralblatt MATH: · Zbl 0025.22704 · doi:10.1215/S0012-7094-41-00832-3
[18] G. RICCI, Principii di una teoria delle forme differenziale quadratiche, Ann. di Mat., 1 (1883), 135-168. · JFM 16.0230.01
[19] L. SCHLAEFLI, Nota alia memoria der Sig. Beltrami, Ann. di Mat., 5(1871-1873), 170-193
[20] I. M. SINGER AND J. A. THORPE, The curvature of 4-dimensional Einstein spaces, Globa Analysis, in h. of K. Kodaira, Princeton Univ. Press, (1966), 355-365. · Zbl 0199.25401
[21] M. SUGIMOTO AND K. SHIOHAMA, On the differentiate pinching problems, Math. Ann., 195 (1971), 1-16. Zentralblatt MATH: · Zbl 0218.53063 · doi:10.1007/BF02059412
[22] S. TANNO, Betti numbers and scalar inequalities, Math. Ann., 190 (1970), 135-148 · Zbl 0195.51303 · doi:10.1007/BF01431496
[23] S. TANNO, Curvature tensors and non-existence of Killing vectors, Tensor, N. S., 2 (1971), 387-394. Zentralblatt MATH: · Zbl 0216.18602
[24] S. TANNO, An inequality for 4-dimensional Kahlerian manifolds, · Zbl 0273.53023 · doi:10.3792/pja/1195519372
[25] T. Y. THOMAS, Imbedding theorems in differential geometry, Bull. Amer. Math. Soc, 4 (1939), 841-850. Zentralblatt MATH: · Zbl 0022.40002 · doi:10.1090/S0002-9904-1939-07100-0
[26] Y. TOMONAGA, Note on Betti numbers of Riemannian manifolds, I, Journ. Math. Soc Japan, 5 (1953), 59-64. · Zbl 0053.11506 · doi:10.2969/jmsj/00510059
[27] Y. TOMONAGA, Euler-Poincare characteristic and sectional curvature, Diff. Geometry i h. of K. Yano, Kinokuniya, Tokyo, (1972), 501-502. · Zbl 0243.53039
[28] A. WEINSTEIN, Positively curved · Zbl 0194.52903
[29] K. YANO AND S. BOCHNER, Curvature and Betti numbers, Ann. Math. Studies, No. 32, Princeton, 1953. · Zbl 0051.39402
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. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.