Kodai Mathematical Journal

Generalized Hopf manifolds, locally conformal Kaehler structures and real hypersurfaces

Sorin Dragomir

Full-text: Open access

Article information

Source
Kodai Math. J., Volume 14, Number 3 (1991), 366-391.

Dates
First available in Project Euclid: 23 January 2006

Permanent link to this document
https://projecteuclid.org/euclid.kmj/1138039462

Digital Object Identifier
doi:10.2996/kmj/1138039462

Mathematical Reviews number (MathSciNet)
MR1131921

Zentralblatt MATH identifier
0751.53020

Subjects
Primary: 53C55: Hermitian and Kählerian manifolds [See also 32Cxx]
Secondary: 53C25: Special Riemannian manifolds (Einstein, Sasakian, etc.) 53C40: Global submanifolds [See also 53B25]

Citation

Dragomir, Sorin. Generalized Hopf manifolds, locally conformal Kaehler structures and real hypersurfaces. Kodai Math. J. 14 (1991), no. 3, 366--391. doi:10.2996/kmj/1138039462. https://projecteuclid.org/euclid.kmj/1138039462


Export citation

References

  • [1] W. BOOTHBY, Some fundamental formulas for Hermitian manifolds with non-vanishing torsion, Am. J. Math., 76 (1954), 509-534.
  • [2] E. BRIESKORN, Beispiele zur Differenzialtopologie von Singulartaten, Inventione Math., 2 (1966), 1-14.
  • [3] E. BRIESKORN AND A. VAN DEVEN, Some complex structures on products o homotopy spheres, Topology, 7 (1968), 389-393,
  • [4] B. Y. CHEN, Geometry of submanifolds, Pure and Appl. Math., M. Dekker, Inc., New York, 1973, 298 p.
  • [5] B. Y. CHEN, Extrinsic spheres in Kaehler manifolds. I-IL, Michigan Math. J., 2 (1977), 97-102.
  • [6] B. Y. CHEN, Extrinsic spheres in compact symmetric spaces are intrinsic spheres, Michigan Math. J., 24 (1977), 265-271
  • [7] B. Y. CHEN AND K. OGIUE, On totally-real submanifolds, Trans. A. M. S., 19 (1974), 257-266.
  • [8] B. Y. CHEN AND K. OGIUE, TWO theorems on Kaehler manifolds, Michigan Math J., 21 (1974), 225-229.
  • [9] B. Y. CHEN AND P. PICCINNI, The canonical foliations of a locally conforma Kaehler manifold, Ann. di Mat. pura appl., 141 (1985), 283-305,
  • [10] J. L. CABRERIZO AND M. F. ANDRES, CR submanifolds of a locally conformal Kaehler manifold, in Diff. Geometry (L. A. Cordero, ed.), Research Notes in Math., 131 (1985), 17-33, Pittman Adv. Publ. progr., Boston-London-Melbourne.
  • [11] A. DOLD, Lectures on algebraic topology, Springer-Verlag, 1980, Berlin-Heidel berg-New York.
  • [12] S. DRAGOMIR, On submanifolds of Hopf manifolds, Israel J. Math., (2) 61 (1988), 98-110
  • [13] S. DRAGOMIR, Cauchy-Riemann submanifolds of locally conformal Kaehler manifolds, MI, Geometriae Dedicata, 28 (1988), 181-197, Atti Sem. Mat. Fis. Univ. Modena, 37 (1989), 1-11.
  • [14] S. DRAGOMIR, Totally-real submanifolds of generalized Hopf manifolds, Le Mate matiche, XL (1987), 3-10.
  • [15] S. DRAGOMIR AND R. GRIMALDI, Isometric immersions of Riemann spaces in real Hopf manifold, Journ. de Mathem. pures appl., 68 (1989), 355-364.
  • [16] R. H. ESCOBALES, Riemannian submersions with totally geodesic fibres, J. Diff Geom., 10 (1975), 253-276.
  • [17] R. H. ESCOBALES, Riemannian submersions from complex projective space, J. Diff. Geom., 13 (1978), 93-107
  • [18] D. FERUS, Totally geodesic foliations, Math. Ann., 188 (1970), 313-316
  • [19] G. GIGANTE, Symmetries on compact pseudohermitian manifolds, Rend. Circol Matem. Palermo, 36 (1987), 148-157.
  • [20] S. GOLDBERG, Curvature and homology, Pure and Appl. Math., Academic Press, 1962, New York-London
  • [21] S. GOLDBERG, On the topology of compact contact manifolds, Tohoku Math. J., 20 (1968), 106-110
  • [22] S. GOLDBERG AND I. VAISMAN, On compact locally conformal Kaehler manifold with non-negative sectional curvature, Ann. Fac. Sci. Toulouse, 2 (1980), 117-123.
  • [23] R. HERMANN, A sufficient condition that a mapping of Riemannian manifolds b a fibre bundle, Proc. A. M. S., 11 (1960), 236-243.
  • [24] S. IANUS, K. MATSUMOTO AND L. ORNEA, Complex hypersurfaces of a generalize Hopf manifold, Publication de Inst. Math., N. S., 42 (1987), 123-129.
  • [25] M. INOUE, On surfaces of classes V0, Inventiones Math., 24 (1974), 269-310
  • [26] T. KASHIWADA AND S. SATO, On harmonic forms in compact locally conformal Kaehler manifolds with parallel Lee form, Ann. Fac. Sci. Kinshasa, Zaire, (1) 6 (1980), 17-29.
  • [27] T. KASHIWADA, Some properties of locally conformal Kaehler manifolds, Hokkaido Math. J., 8 (1979), 191-198.
  • [28] S. KOBAYASHI AND K. NOMIZU, Foundations of differential geometry, Interscience Publ., New York, vol. MI, 1963, 1969.
  • [29] Y. MATSUSHIMA, Vector bundle valued harmonic forms and immersions of Riemannian manifolds, Osaka J. Math., 8 (1971), 1-13.
  • [30] K. MATSUMOTO, On submanifolds of locally conformal Kaehler manifolds, Bull Yamagata Univ., (1) 11 (1984), 33-38.
  • [31] K. MATSUMOTO, On CR submanifolds of locally conformal Kaehler manifolds, J. Korean Math. Soc, (1) 21 (1984), 49-61
  • [32] K. MATSUMOTO, On locally conformal Kaehler space forms, Internat. J. Math & Math. Sci., (1) 8 (1985), 69-74.
  • [33] K. MATSUMOTO, On CR submanifolds of locally conformal Kaehler manifolds II., Tensor, N. S., 45 (1987), 144-150.
  • [34] J. W. MILNOR AND J. D. STASHEFF, Characteristic classes, Ann. of Math. Stud., Princeton Univ. Press, No. 76, 1974, New Jersey
  • [35] J. R. MUNKRES, Elements of algebraic topology, Addison-Wesley Publ. Co., Inc., 1984, Massachusetts
  • [36] M. NAMBA, Automorphism groups of Hopf surfaces, Tohoku Math. J., 26 (1974), 133-157
  • [37] K. NOMIZU, On the spaces of generalized curvature tensor fields and second fundamental forms, Osaka J. Math., 8 (1971), 21-28.
  • [38] B. O'NEILL, The fundamental equations of a submersion, Michigan Math. J., (4 13 (1966), 459-469.
  • [39] M. OBATA, Certain conditions for a Riemannian manifold to be isometric to sphere, J. Math. Soc. Japan, 14 (1962), 333-340.
  • [40] K. OGIUE, On invariant immersions, Ann. Matem. pura appl., LXXX (1968), 387-397
  • [41] L. ORNEA, On CR submanifolds of locally conformal Kaehler manifolds, Demon stratio Math., (4) 29 (1986), 863-869.
  • [42] M. OKUMURA, Contact hypersurfaces in certain Kaehlerian manifolds, Tohok Math. J., (1) 18 (1966), 74-102.
  • [43] C. REISCHER AND I. VAISMAN, Local similarity manifolds, Ann. Matem. pur appl., 35 (1983), 279-292.
  • [44] P. J. RYAN, Homogeneity and some curvature conditions for hypersurfaces, To hoku Math. J., 21 (1969), 363-388.
  • [45] S. SASAKI AND C. J. Hsu, On a property of Brieskorn manifolds, Tohoku Math J., 28 (1976), 67-78.
  • [46] Y. TASHIRO, On contact structures of hypersurfaces in almost complex manifolds I-IL, Tohoku Math. J., 15 (1963), 62-78, 167-175.
  • [47] F. TRICERRI, Some examples of locally conformal Kaehler manifolds, Rend. Sem Mat. Univers. Politecn. Torino, (1) 40 (1982), 81-92.
  • [48] H. TSUKADA, Hopf manifolds and spectral geometry, Trans. A. M. S., (2) 27 (1982), 609-621.
  • [49] I. VAISMAN, Locally conformal Kaehler manifolds with parallel Lee form, Rendi conti di Matem., 12 (1979), 263-284.
  • [50] I. VAISMAN, Generalized Hopf manifolds, Geometriae Dedicata, 13 (1982), 231-255
  • [51] I. VAISMAN, A theorem on compact locally conformal Kaehler manifolds, Proc A. M. S., (2) 75 (1979), 279-283.
  • [52] I. VAISMAN, Some curvature properties of locally conformal Kaehler manifolds, Trans. A. M. S., (2) 259 (1980), 439-447
  • [53] I. VAISMAN, Some curvature properties of complex surfaces, Ann. Matem. pur appl., XXXII (1982), 1-18.
  • [54] I. VAISMAN, On locally and globally conformal Kaehler manifolds, Trans. A. M. S., (2) 262 (1980), 533-542
  • [55] B. WATSON, The first Betti numbers of certain locally trivial fibre spaces. Bull A. M. S., (3) 78 (1972), 392-393.
  • [56] K. YANA AND M. KON, CR submanifolds of Kaehlerian and Sasakian manifolds, Progress in Math., vol. 30, Birkhauser, 1983, Boston-Basel-Stuttgart