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On manifolds admitting metrics which are locally conformal to cosymplectic metrics: their canonical foliations, Boothby-Wang fiberings, and real homology type

Authors 1, 2

Affiliations

  1. Università Degli Studi di Bari, Dipartimento di Matematica, I-70125 Bari, Italy
  2. Mathematics Department, State University of New York, At Stony Brook, Stony Brook, New York 11794-3651, U.S.A.

Bibliography

  1. D. E. Blair, The theory of quasi-Sasakian structures, J. Differential Geom. 1 (1967), 331-345.
  2. D. E. Blair, Contact Manifolds in Riemannian Geometry, Lecture Notes in Math. 509, Springer, 1976.
  3. D. E. Blair and S. Goldberg, Topology of almost contact manifolds, J. Differential Geom. 1 (1967), 347-354.
  4. D. E. Blair, C. D. Ludden and K. Yano, Differential geometric structures on principal toroidal bundles, Trans. Amer. Math. Soc. 181 (1973), 175-184.
  5. W. M. Boothby and H. C. Wang, On contact manifolds, Ann. of Math. (3) 68 (1958), 721-734.
  6. S. Dragomir, On submanifolds of Hopf manifolds, Israel J. Math. (2) 61 (1988), 98-110.
  7. S. Dragomir, Cauchy-Riemann submanifolds of locally conformal Kaehler manifolds. I-II, Geom. Dedicata 28 (1988), 181-197, Atti Sem. Mat. Fis. Univ. Modena 37 (1989), 1-11.
  8. S. Dragomir and L. M. Abatangelo, Principal toroidal bundles over Cauchy-Riemann products, Internat. J. Math. Math. Sci. (2) 13 (1990), 299-310.
  9. S. Dragomir and R. Grimaldi, Isometric immersions of Riemann spaces in a real Hopf manifold, J. Math. Pures Appl. 68 (1989), 355-364.
  10. S. I. Goldberg, Curvature and Homology, Academic Press, New York 1962.
  11. S. I. Goldberg, Totally geodesic hypersurfaces of Kaehler manifolds, Pacific J. Math. (2) 27 (1968), 275-281.
  12. M. Inoue, On surfaces of class VII_0, Invent. Math. 24 (1974), 269-310.
  13. S. Kobayashi and K. Nomizu, Foundations of Differential Geometry, Interscience, Vols. I-II, New York 1963, 1969.
  14. P. Libermann, Sur les structures presque complexes et autres structures infinité- simales régulières, Bull. Soc. Math. France 83 (1955), 195-224.
  15. Z. Olszak, On almost cosymplectic manifolds, Kodai Math. J. 1 (1981), 239-250.
  16. Z. Olszak, Locally conformal almost cosymplectic manifolds, Colloq. Math. 57 (1989), 73-87.
  17. Z. Olszak, Normal almost contact metric manifolds of dimension 3, Ann. Polon. Math. 47 (1986), 41-50.
  18. R. S. Palais, A global formulation of the Lie theory of transformation groups, Mem. Amer. Math. Soc. 22 (1957).
  19. C. Reischer and I. Vaisman, Local similarity manifolds, Ann. Mat. Pura Appl. 135 (1983), 279-292.
  20. J. L. Synge, On the connectivity of spaces of positive curvature, Quart. J. Math. Oxford Ser. 7 (1936), 316-320.
  21. S. Tanno, A theorem on regular vector fields and its applications to almost contact structures, Tôhoku Math. J. 17 (1965), 235-243.
  22. S. Tanno, Quasi-Sasakian structures of rank 2p+1, J. Differential Geom. 5 (1971), 317-324.
  23. F. Tricerri, Some examples of locally conformal Kaehler manifolds, Rend. Sem. Mat. Univ. Politec. Torino 40 (1982), 81-92.
  24. I. Vaisman, Locally conformal Kaehler manifolds with parallel Lee form, Rend. Mat. 12 (1979), 263-284.
  25. I. Vaisman, Conformal change of almost contact metric structures, in: Proc. Conference on Differential Geometry, Haifa 1979, Lecture Notes in Math. 792, Springer, 1980.
  26. K. Yano and M. Kon, Structures On Manifolds, Ser. Pure Math., World Sci., 1984.
Colloquium Mathematicum
1993/64/1
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Pages:
29-40
Main language of publication
English
Received
1991-01-21
Published
1993
Exact and natural sciences