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On characteristic classes of conformal and projective foliations
Shigeyuki MORITA
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Shigeyuki MORITA
Department of Mathematics Osaka City University Department of Mathematics College of General Education University of Tokyo
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1979 Volume 31 Issue 4 Pages 693-718
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- Published: 1979 Received: February 15, 1978 Available on J-STAGE: October 20, 2006 Accepted: - Advance online publication: - Revised: -
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Correction information
Date of correction: October 20, 2006 Reason for correction: - Correction: SUBTITLE Details: Wrong : Dedicated to Professor A. Komatu on his 70th birthday
Date of correction: October 20, 2006 Reason for correction: - Correction: CITATION Details: Wrong : 1) R. Bott, On a topological obstruction to integrability, Global analysis (Proc. Sympos. Pure Math., Vol. XVI, Berkeley, California, 1968), Amer. Math. Soc., 1970, 127-131.
2) R. Bott, Lectures on characteristic classes and foliations, Lectures on algebraic and differential topology, Lecture Notes in Math., No. 279, 1-94, Springer, Berlin, 1970.
3) R. Bott, On characteristic classes in the framework of Gelfand-Fuks cohomology, Colloque analyse et topologie, Astérisque 32-33, 113-139, 1976.
4) R. Bott and A. Haefliger, On characteristic classes of Γ-foliations, Bull. Amer. Math. Soc., 78 (1972), 1039-1044.
5) H. Cartan, Notions d'algèbre différentielle, Colloque de Topologie, Bruxelles, 15-27, 1950.
6) S. Chern and J. Simons, Characteristic forms and geometric invariants, Ann. of Math., 99 (1974), 48-69.
7) D. B. Fuchs, Non-trivialité des classes caractéristiques de g-structures. Application aux classes caractéristiques de feuilletages, C. R. Acad. Sci. Paris, 284 (1977), 1017-1019.
8) A. Haefliger, Homotopy and integrability, Manifolds-Amsterdam 1970, Lecture Notes in Math., No. 197, 133-166, Springer, Berlin, 1971.
9) J. Heitsch, Deformations of secondary characteristic classes, Topology, 12 (1973), 381-388.
10) G. Hochschild and J. P. Serre, Cohomology of Lie algebras, Ann. of Math., 57 (1953), 591-603.
11) F. Kamber and P. Tondeur, Cohomologie des algèbres de Weil relatives tronquées, C. R. Acad. Sci. Paris, 276 (1973), 459-462; Classes caractéristiques généralisées des fibrés feuilletés localement homogènes, C. R. Acad. Sci. Paris, 279 (1974), 847-850; Quelques classes caractéristiques généralisées nontriviales de fibrés feuilletés, C.R. Acad. Sci. Paris, 279 (1974), 921-924.
12) F. Kamber and P. Tondeur, Characteristic invariants of foliated bundles, Manuscripta Math., 11 (1974), 51-89.
13) F. Kamber and P. Tondeur, Foliated bundles and characteristic classes, Lecture Notes in Math., No. 493, Springer, Berlin, 1975.
14) S. Kobayashi, Transformation groups in differential geometry, Springer, Berlin, 1972.
15) S. Kobayashi and T. Nagano, On filtered Lie algebras and geometric structures I, J. Math. Mech., 13 (1964), 875-908.
16) C. Lazarov and J. Pasternack, Secondary characteristic classes for Riemannian foliations, J. Differential Geometry, 11 (1976), 365-385.
17) C. Lazarov and J. Pasternack, Residues and characteristic classes for Riemannian foliations, J. Differential Geometry, 11 (1976), 599-612.
18) S. Morita, On characteristic classes of Riemannian foliations, Osaka J. Math., 16 (1979), 161-172.
19) S. Morita, Cartan connection and characteristic classes of foliations, Proc. Japan Acad., 53A (1977), 211-214.
20) M. Mostow and J. Perchik, Notes on Gelf and Fuks Cohomology and characteristic classes, Proc, of the 11th Annual Holiday Symposium at New Mexico State University 1973, New Mexico State University, 1975.
21) S. Nishikawa, Residues and secondary characteristic classes for projective foliations, Proc. Japan Acad., 54A (1978), 79-82.
22) S. Nishikawa and H. Sato, On characteristic classes of Riemannian, conformal and projective foliations, J. Math. Soc. Japan, 28 (1976), 223-241.
23) S. Nishikawa and M. Takeuchi, Γ-foliations and semisimple flat homogeneous spaces, to appear.
24) T. Ochiai, Geometry associated with semi-simple flat homogeneous spaces, Trans. Amer. Math. Soc., 152 (1970), 1-33.
25) J. Pasternack, Foliations and compact Lie group actions, Comment. Math. Helv., 46 (1971), 467-477.
26) M. Takeuchi, On foliations with the structure group of automorphisms of a geometric structure, preprint.
27) H. Weyl, Classical groups, Princeton, 1946.
28) K. Yamato, Examples of foliations with non-trivial exotic characteristic classes, Osaka J. Math,, 12 (1975), 407-417.
29) K. Yamato, On exotic characteristic classes of conformal and projective foliations, to appear.
Right : [1] R. Bott, On a topological obstruction to integrability, Global analysis (Proc. Sympos. Pure Math., Vol. XVI, Berkeley, California, 1968), Amer. Math. Soc., 1970, 127-131.
[2] R. Bott, Lectures on characteristic classes and foliations, Lectures on algebraic and differential topology, Lecture Notes in Math., No. 279, 1-94, Springer, Berlin, 1970.
[3] R. Bott, On characteristic classes in the framework of Gelfand-Fuks cohomology, Colloque analyse et topologie, Astérisque 32-33, 113-139, 1976.
[4] R. Bott and A. Haefliger, On characteristic classes of Γ-foliations, Bull. Amer. Math. Soc., 78 (1972), 1039-1044.
[5] H. Cartan, Notions d'algèbre différentielle, Colloque de Topologie, Bruxelles, 15-27, 1950.
[6] S. Chern and J. Simons, Characteristic forms and geometric invariants, Ann. of Math., 99 (1974), 48-69.
[7] D. B. Fuchs, Non-trivialité des classes caractéristiques de g-structures. Application aux classes caractéristiques de feuilletages, C. R. Acad. Sci. Paris, 284 (1977), 1017-1019.
[8] A. Haefliger, Homotopy and integrability, Manifolds-Amsterdam 1970, Lecture Notes in Math., No. 197, 133-166, Springer, Berlin, 1971.
[9] J. Heitsch, Deformations of secondary characteristic classes, Topology, 12 (1973), 381-388.
[10] G. Hochschild and J. P. Serre, Cohomology of Lie algebras, Ann. of Math., 57 (1953), 591-603.
[11] F. Kamber and P. Tondeur, Cohomologie des algèbres de Weil relatives tronquées, C. R. Acad. Sci. Paris, 276 (1973), 459-462; Classes caractéristiques généralisées des fibrés feuilletés localement homogènes, C. R. Acad. Sci. Paris, 279 (1974), 847-850; Quelques classes caractéristiques généralisées nontriviales de fibrés feuilletés, C. R. Acad. Sci. Paris, 279 (1974), 921-924.
[12] F. Kamber and P. Tondeur, Characteristic invariants of foliated bundles, Manuscripta Math., 11 (1974), 51-89.
[13] F. Kamber and P. Tondeur, Foliated bundles and characteristic classes, Lecture Notes in Math., No. 493, Springer, Berlin, 1975.
[14] S. Kobayashi, Transformation groups in differential geometry, Springer, Berlin, 1972.
[15] S. Kobayashi and T. Nagano, On filtered Lie algebras and geometric structures I, J. Math. Mech., 13 (1964), 875-908.
[16] C. Lazarov and J. Pasternack, Secondary characteristic classes for Riemannian foliations, J. Differential Geometry, 11 (1976), 365-385.
[17] C. Lazarov and J. Pasternack, Residues and characteristic classes for Riemannian foliations, J. Differential Geometry, 11 (1976), 599-612.
[18] S. Morita, On characteristic classes of Riemannian foliations, Osaka J. Math., 16 (1979), 161-172.
[19] S. Morita, Cartan connection and characteristic classes of foliations, Proc. Japan Acad., 53A (1977), 211-214.
[20] M. Mostow and J. Perchik, Notes on Gelf and Fuks Cohomology and characteristic classes, Proc. of the 11th Annual Holiday Symposium at New Mexico State University 1973, New Mexico State University, 1975.
[21] S. Nishikawa, Residues and secondary characteristic classes for projective foliations, Proc. Japan Acad., 54A (1978), 79-82.
[22] S. Nishikawa and H. Sato, On characteristic classes of Riemannian, conformal and projective foliations, J. Math. Soc. Japan, 28 (1976), 223-241.
[23] S. Nishikawa and M. Takeuchi, Γ-foliations and semisimple flat homogeneous spaces, to appear.
[24] T. Ochiai, Geometry associated with semi-simple flat homogeneous spaces, Trans. Amer. Math. Soc., 152 (1970), 1-33.
[25] J. Pasternack, Foliations and compact Lie group actions, Comment. Math. Helv., 46 (1971), 467-477.
[26] M. Takeuchi, On foliations with the structure group of automorphisms of a geometric structure, preprint.
[27] H. Weyl, Classical groups, Princeton, 1946.
[28] K. Yamato, Examples of foliations with non-trivial exotic characteristic classes, Osaka J. Math., 12 (1975), 407-417.
[29] K. Yamato, On exotic characteristic classes of conformal and projective foliations, to appear.
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