On characteristic classes of riemannian, conformal and projective foliations

Seiki NISHIKAWA; Hajime SATO

doi:10.2969/jmsj/02820223

Seiki NISHIKAWA, Hajime SATO

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1976 Volume 28 Issue 2 Pages 223-241

DOI https://doi.org/10.2969/jmsj/02820223

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Published: 1976 Received: October 05, 1974 Available on J-STAGE: October 20, 2006 Accepted: - Advance online publication: - Revised: -
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Date of correction: October 20, 2006 Reason for correction: - Correction: AUTHOR Details: Wrong : Seiki NISHIKAWA¹⁾, Hahune SATO¹⁾
Right : Seiki NISHIKAWA¹⁾, Hajime SATO¹⁾

Date of correction: October 20, 2006 Reason for correction: - Correction: AFFILIATION Details: Wrong :
1) Department of Mathematics Tohoku University

Right :
1) Department of Mathematics Tôhoku University

Date of correction: October 20, 2006 Reason for correction: - Correction: CITATION Details: Wrong : 1) P. Baum and R. Bott, Singularities of holomorphic foliations, J. Differential Geometry, 7 (1972), 279-342.
2) A. Borel, Compact Clifford-Klein forms of symmetric spaces, Topology, 2 (1963), 112-122.
3) A. Borel and F. Hirzebruch, Characteristic classes and homogeneous spaces, Amer. J. Math., 80 (1958), 458-538; 81 (1959), 315-382; 82 (1960), 491-504.
4) R. Bott, On a topological obstruction to integrability, Proc. Symp. Pure Math., Amer. Math. Soc., Providence, R. I., 16 (1970), 127-131.
5) R. Bott, On topological obstructions to integrability, Actes Congrès Intern. Math. (Nice 1970), vol. 1, Gauthier-Villars, Paris, 1971, 27-36.
6) R. Bott, Lectures on characteristic classes and foliations, Notes by L. Conlon, Mexico, 1971, Springer Lecture Notes in Math., no. 279, Springer N. Y., 1972, 1-80.
7) R. Bott and A. Haefliger, On characteristic classes of Γ-foliations, Bull. Amer. Math. Soc., 78 (1972), 1039-1044.
8) H. Cartan, Notions d'algebre différentielle; application aux groupes de Lie et aux variétés où-opére un groupes de Lie, Colloque Topologie, Bruxelles, 1950, 15-27.
9) H. Cartan, La transgression dans un groupe de Lie et dans un espace fibré principal, Colloque Topologie, Bruxelles, 1950, 15-27.
10) D. B. Fuks, Characteristic classes of foliations, Russian Math. Surveys, 28 (1973), 1-16.
11) C. Godbillon and J. Vey, Un invariant des feuilletages de codimension 1, C. R. Acad. Sci. Paris, Sér. A, 273 (1971), 92-95.
12) A. Haefliger, Variétés feuilletées, Ann. Scuola Norm. Sup. Pisa, 16 (1962), 367-397.
13) A. Haefliger, Sur les classes charactéristiques des feuilletages, Séminaire Bourbaki, 1971/72, no. 412, 239-260.
14) S. Kobayashi, Transformation groups in differential geometry, Springer-Verlag, Berlin-Heidelberg-New York, 1972.
15) S. Kobayashi and T. Nagano, On projective connections, J. Math. Mech., 13 (1964), 215-236.
16) S. Kobayashi and K. Nomizu, Foundations of differential geometry, vol. I, vol. II, Interscience, New York, 1963, 1969.
17) H. B. Lawson, Jr., Foliations, Bull. Amer. Math. Soc., 80 (1974), 369-418.
18) M. Obata, Conformal transformations of Riemannian manifolds, J. Differential Geometry, 4 (1970), 311-333.
19) T. Ochiai, Geometry associated with semisimple flat homogeneous spaces, Trans. Amer. Math. Soc., 152 (1970), 159-193.
20) K. Ogiue, Theory of conformal connections, Kodai Math. Sem. Rep., 19 (1967), 193-224.
21) J. Pasternack, Foliations and compact Lie group actions, Comm. Math. Helv., 46 (1971), 467-477.
22) G. Reeb, Sur certains propriétés topologiques des variétés feuilletées, Actualités Sci. Indust., Hermann, Paris, 1952, 91-154; 157-158.
23) B. L. Reinhart, Foliated manifolds with bundle-like metrics, Ann. of Math., 69 (1959), 119-132.
24) N. Tanaka, Projective connections and projective transformations, Nagoya Math. J., 11 (1957), 1-24.
25) N. Tanaka, Conformal connections and conformal transformations, Trans. Amer. Math. Soc., 92 (1959), 168-190.
26) W. Thurston, Foliations and groups of diffeomorphisms, Bull. Amer. Math. Soc., 80 (1974), 304-307.
27) P. Tomter, Anosov flows on infra-homogeneous spaces, Proc. Symp. Pure Math., Amer. Math. Soc., Providence, R. I., 14 (1970), 299-327.
28) K. Yamato, Examples of foliations with non trivial exotic characteristic classes, Proc. Japan Acad., 50 (1974), 127-129.
29) M. S. Narasimhan and S. Ramanan, Existence of universal connections, Amer. J. Math., 83 (1961), 563-572; II, 85 (1963), 223-231.

Right : [1] P. Baum and R. Bott, Singularities of holomorphic foliations, J. Differential Geometry, 7 (1972), 279-342.
[2] A. Borel, Compact Clifford-Klein forms of symmetric spaces, Topology, 2 (1963), 112-122.
[3] A. Borel and F. Hirzebruch, Characteristic classes and homogeneous spaces, Amer. J. Math., 80 (1958), 458-538; 81 (1959), 315-382; 82 (1960), 491-504.
[4] R. Bott, On a topological obstruction to integrability, Proc. Symp. Pure Math., Amer. Math. Soc., Providence, R. I., 16 (1970), 127-131.
[5] R. Bott, On topological obstructions to integrability, Actes Congrès Intern. Math. (Nice 1970), vol. 1, Gauthier-Villars, Paris, 1971, 27-36.
[6] R. Bott, Lectures on characteristic classes and foliations, Notes by L. Conlon, Mexico, 1971, Springer Lecture Notes in Math., no. 279, Springer N. Y., 1972, 1-80.
[7] R. Bott and A. Haefliger, On characteristic classes of Γ-foliations, Bull. Amer. Math. Soc., 78 (1972), 1039-1044.
[8] H. Cartan, Notions d'algebre différentielle; application aux groupes de Lie et aux variétés où opère un groupes de Lie, Colloque Topologie, Bruxelles, 1950, 15-27.
[9] H. Cartan, La transgression dans un groupe de Lie et dans un espace fibré principal, Colloque Topologie, Bruxelles, 1950, 15-27.
[10] D. B. Fuks, Characteristic classes of foliations, Russian Math. Surveys, 28 (1973), 1-16.
[11] C. Godbillon and J. Vey, Un invariant des feuilletages de codimension 1, C. R. Acad. Sci. Paris, Sér. A, 273 (1971), 92-95.
[12] A. Haefliger, Variétés feuilletées, Ann. Scuola Norm. Sup. Pisa, 16 (1962), 367-397.
[13] A. Haefliger, Sur les classes charactéristiques des feuilletages, Séminaire Bourbaki, 1971/72, no. 412, 239-260.
[14] S. Kobayashi, Transformation groups in differential geometry, Springer-Verlag, Berlin-Heidelberg-New York, 1972.
[15] S. Kobayashi and T. Nagano, On projective connections, J. Math. Mech., 13 (1964), 215-236.
[16] S. Kobayashi and K. Nomizu, Foundations of differential geometry, vol. I, vol. II, Interscience, New York, 1963, 1969.
[17] H. B. Lawson, Jr., Foliations, Bull. Amer. Math. Soc., 80 (1974), 369-418.
[18] M. Obata, Conformal transformations of Riemannian manifolds, J. Differential Geometry, 4 (1970), 311-333.
[19] T. Ochiai, Geometry associated with semisimple flat homogeneous spaces, Trans. Amer. Math. Soc., 152 (1970), 159-193.
[20] K. Ogiue, Theory of conformal connections, Kodai Math. Sem. Rep., 19 (1967), 193-224.
[21] J. Pasternack, Foliations and compact Lie group actions, Comm. Math. Helv., 46 (1971), 467-477.
[22] G. Reeb, Sur certains propriétés topologiques des variétés feuilletées, Actualités Sci. Indust., Hermann, Paris, 1952, 91-154; 157-158.
[23] B. L. Reinhart, Foliated manifolds with bundle-like metrics, Ann. of Math., 69 (1959), 119-132.
[24] N. Tanaka, Projective connections and projective transformations, Nagoya Math. J., 11 (1957), 1-24.
[25] N. Tanaka, Conformal connections and conformal transformations, Trans. Amer. Math. Soc., 92 (1959), 168-190.
[26] W. Thurston, Foliations and groups of diffeomorphisms, Bull. Amer. Math. Soc., 80 (1974), 304-307.
[27] P. Tomter, Anosov flows on infra-homogeneous spaces, Proc. Symp. Pure Math., Amer. Math. Soc., Providence, R. I., 14 (1970), 299-327.
[28] K. Yamato, Examples of foliations with non trivial exotic characteristic classes, Proc. Japan Acad., 50 (1974), 127-129.
[29] M. S. Narasimhan and S. Ramanan, Existence of universal connections, Amer. J. Math., 83 (1961), 563-572; II, 85 (1963), 223-231.

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