Harmonic forms and Betti numbers of certain contact Riemannian manifolds

Shûkichi TANNO

doi:10.2969/jmsj/01930308

Shûkichi TANNO

著者情報

ジャーナルフリー

1967 年 19 巻 3 号 p. 308-316

DOI https://doi.org/10.2969/jmsj/01930308

詳細

Published: 1967 Received: 1966/07/07 Available on J-STAGE: 2006/09/26 Accepted: - Advance online publication: - Revised: -
訂正情報
訂正日: 2006/09/26 訂正理由: - 訂正箇所: 所属機関情報訂正内容: 訂正前 :
1) Mathematical Institute Tohoku University

訂正後 :
1) Mathematical Institute Tôhoku University

訂正日: 2006/09/26 訂正理由: - 訂正箇所: 引用文献情報訂正内容: Wrong : 1) W. M. Boothby and H. C. Wang, On contact manifolds, Ann. of Math., 68 (1958), 721-734.
2) S. S. Chern and E. Spanier, The homology structure of sphere bundles, Proc. Nat. Acad. Sci. U.S.A., 36 (1950), 248-255.
3) T. Fujitani, Complex-valued differential forms on a normal contact manifold, Tohoku Math. J., 18 (1966), 349-361.
4) S. Goldberg, Rigidité de variétés de contact à coubure positive, C. R. Acad. Sci. Paris, 261 (1965), 1936-1939.
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. Kobayoshi, Topology of positively pinched Kaehler manifolds, Tohoku Math. J., 15 (1963), 121-139.
8) K. Ogiue, On fiberings of almost contact manifolds, Kodai Math. Sem. Rep., 17 (1965), 53-61.
9) M. Okumura, Some remarks on space with a certain contact structure, Tohoku Math. J., 14 (1962), 135-145.
10) S. Sasaki, On differentiable manifolds with certain structures which are closely related to almost contact structure, I, Tohoku Math. J., 12 (1960), 459-476.
11) S. Sasaki, Almost contact manifolds, Lecture note, Tohoku Univ., 1965.
12) J.P. Serre, Homologie singuliére des espaces fibrés, Ann. of Math., 54 (1951), 425-505.
13) S. Tachibana, On harmonic tensors in compact Sasakian spaces, Tohoku Math. J., 17 (1965), 271-284.
14) S. Tanno, A theorem on regular vector fields and its applications to almost contact structure, Tohoku Math. J., 17 (1965), 235-238.
15) S. Tanno, Partially conformal transformations with respect to (m-1)-dimensional distributions of m-dimensional Riemannian manifolds, Tohoku Math. J., 17 (1965), 358-409.
16) K. Yano and S. Bochner, Curvature and Betti numbers, Ann. of Math. Studies 32, Princeton, 1953.

Right : [1] W. M. Boothby and H. C. Wang, On contact manifolds, Ann. of Math., 68 (1958), 721-734.
[2] S. S. Chern and E. Spanier, The homology structure of sphere bundles, Proc. Nat. Acad. Sci. U. S. A., 36 (1950), 248-255.
[3] T. Fujitani, Complex-valued differential forms on a normal contact manifold, Tôhoku Math. J., 18 (1966), 349-361.
[4] S. Goldberg, Rigidité de variétés de contact à coubure positive, C. R. Acad. Sci. Paris, 261 (1965), 1936-1939.
[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. Kobayoshi, Topology of positively pinched Kaehler manifolds, Tôhoku Math. J., 15 (1963), 121-139.
[8] K. Ogiue, On fiberings of almost contact manifolds, Kodai Math. Sem. Rep., 17 (1965), 53-61.
[9] M. Okumura, Some remarks on space with a certain contact structure, Tôhoku Math. J., 14 (1962), 135-145.
[10] S. Sasaki, On differentiable manifolds with certain structures which are closely related to almost contact structure, I, Tôhoku Math. J., 12 (1960), 459-476.
[11] S. Sasaki, Almost contact manifolds, Lecture note, Tôhoku Univ., 1965.
[12] J. P. Serre, Homologie singuliére des espaces fibrés, Ann. of Math., 54 (1951), 425-505.
[13] S. Tachibana, On harmonic tensors in compact Sasakian spaces, Tôhoku Math. J., 17 (1965), 271-284.
[14] S. Tanno, A theorem on regular vector fields and its applications to almost contact structure, Tôhoku Math. J., 17 (1965), 235-238.
[15] S. Tanno, Partially conformal transformations with respect to (m-1)-dimensional distributions of m-dimensional Riemannian manifolds, Tôhoku Math. J., 17 (1965), 358-409.
[16] K. Yano and S. Bochner, Curvature and Betti numbers, Ann. of Math. Studies 32, Princeton, 1953.

訂正日: 2006/09/26 訂正理由: - 訂正箇所: PDFファイル訂正内容: -

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