A formula on some odd-dimensional Riemannian manifolds related to the Gauss-Bonnet formula

Shûkichi TANNO

doi:10.2969/jmsj/02420204

Shûkichi TANNO

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JOURNAL FREE ACCESS

1972 Volume 24 Issue 2 Pages 204-212

DOI https://doi.org/10.2969/jmsj/02420204

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Published: 1972 Received: August 20, 1971 Available on J-STAGE: September 29, 2006 Accepted: - Advance online publication: - Revised: -
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Date of correction: September 29, 2006 Reason for correction: - Correction: AFFILIATION Details: Wrong :
1) Mathematical Institute Tohoku University

Right :
1) Mathematical Institute Tôhoku University

Date of correction: September 29, 2006 Reason for correction: - Correction: CITATION Details: Wrong : 1) W. M. Boothby and H. C. Wang, On contact manifolds, Ann. of Math., 68 (1958), 721-734.
2) S.S. Chern, A simple intrinsic proof of the Gauss-Bonnet theorem for closed Riemannian manifolds, Ann. of Math., 45 (1944), 747-752.
3) S.S. Chern, On the curvatura integra in a Riemannian manifold, Ann. of Math., 46 (1945), 674-684.
4) S.S. Chern and E. Spanier, The homology structure of sphere bundles, Proc. Nat. Acad. Sci. U.S.A., 36 (1950), 248-255.
5) Y. Hatakeyama, Some notes on differentiable manifolds with almost contact structures, Tohoku Math. J., 15 (1963), 176-181.
6) Y. Hatakeyama, Y. Ogawa and S. Tanno, Some properties of manifolds with contact metric structure, Tohoku Math. J., 15 (1963), 42-48.
7) S. Kobayashi, Topology of positively pinched Kähler manifolds, Tohoku Math. J., 15(1963), 121-139.
8) S. Sasaki and Y. Hatakeyama, On differentiable manifolds with contact metric structures, J. Math. Soc. Japan, 14 (1962), 249-271.
9) J. P. Serre, Homologie singuliére des espaces fibrés, Ann. of Math., 54 (1951), 425-505.
10) S. Tanno, Sur une variété de K-contact métrique de dimension 3, C.R. Acad. Sci. Paris, 263 (1966), 317-319.
11) S. Tanno, Harmonic forms and Betti numbers of certain contact Riemannian manifolds, J. Math. Soc. Japan, 19 (1967), 308-316.
12) S. Tanno, Sasakian manifolds with constant φ-holomorphic sectional curvature, Tohoku Math. J., 21 (1969), 501-507.
13) J.A. Wolf, A contact structure for odd dimensional spherical space forms, Proc. Amer. Math. Soc., 19 (1968), 196.

Right : [1] W. M. Boothby and H. C. Wang, On contact manifolds, Ann. of Math., 68 (1958), 721-734.
[2] S. S. Chern, A simple intrinsic proof of the Gauss-Bonnet theorem for closed Riemannian manifolds, Ann. of Math., 45 (1944), 747-752.
[3] S. S. Chern, On the curvatura integra in a Riemannian manifold, Ann. of Math., 46 (1945), 674-684.
[4] S. S. Chern and E. Spanier, The homology structure of sphere bundles, Proc. Nat. Acad. Sci. U. S. A., 36 (1950), 248-255.
[5] Y. Hatakeyama, Some notes on differentiable manifolds with almost contact structures, Tôhoku Math. J., 15 (1963), 176-181.
[6] Y. Hatakeyama, Y. Ogawa and S. Tanno, Some properties of manifolds with contact metric structure, Tôhoku Math. J., 15 (1963), 42-48.
[7] S. Kobayashi, Topology of positively pinched Kähler manifolds, Tôhoku Math. J., 15 (1963), 121-139.
[8] S. Sasaki and Y. Hatakeyama, On differentiable manifolds with contact metric structures, J. Math. Soc. Japan, 14 (1962), 249-271.
[9] J. P. Serre, Homologie singuliére des espaces fibrés, Ann. of Math., 54 (1951), 425-505.
[10] S. Tanno, Sur une variété de K-contact métrique de dimension 3, C. R. Acad. Sci. Paris, 263 (1966), 317-319.
[11] S. Tanno, Harmonic forms and Betti numbers of certain contact Riemannian manifolds, J. Math. Soc. Japan, 19 (1967), 308-316.
[12] S. Tanno, Sasakian manifolds with constant φ-holomorphic sectional curvature, Tohoku Math. J., 21 (1969), 501-507.
[13] J. A. Wolf, A contact structure for odd dimensional spherical space forms, Proc. Amer. Math. Soc., 19 (1968), 196.

Date of correction: September 29, 2006 Reason for correction: - Correction: PDF FILE Details: -

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