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1996 | 70 | 2 | 165-179
Tytuł artykułu

CR-submanifolds of locally conformal Kaehler manifolds and Riemannian submersions

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
We consider a Riemannian submersion π: M → N, where M is a CR-submanifold of a locally conformal Kaehler manifold L with the Lee form ω which is strongly non-Kaehler and N is an almost Hermitian manifold. First, we study some geometric structures of N and the relation between the holomorphic sectional curvatures of L and N. Next, we consider the leaves M of the foliation given by ω = 0 and give a necessary and sufficient condition for M to be a Sasakian manifold.
Słowa kluczowe
Rocznik
Tom
70
Numer
2
Strony
165-179
Opis fizyczny
Daty
wydano
1996
otrzymano
1995-03-03
Twórcy
autor
  • Department of Mathematics, Akita National College of Technology, 1-1, Bunkyo-cho Iijima, Akita 011, Japan
Bibliografia
  • [1] R. L. Bishop and S. I. Goldberg, On the topology of positively curved Kaehler manifolds II, Tôhoku Math. J. 17 (1965), 310-318.
  • [2] D. E. Blair, Contact Manifolds in Riemannian Geometry, Lecture Notes in Math. 509, Springer, Berlin, 1976.
  • [3] D. E. Blair and B. Y. Chen, On CR-submanifolds of Hermitian manifolds, Israel J. Math. 34 (1979), 353-363.
  • [4] B. Y. Chen and L. Vanhecke, Isometric, holomorphic and symplectic reflections, Geom. Dedicata 29 (1989), 259-277.
  • [5] S. Dragomir, On submanifolds of Hopf manifolds, Israel J. Math. (2) 61 (1988), 98-110.
  • [6] 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.
  • [7] S. Kobayashi, Submersions of CR submanifolds, Tôhoku Math. J. 89 (1987), 95-100.
  • [8] S. Kobayashi and K. Nomizu, Foundations of Differential Geometry, Vols. 1, 2, Interscience Publishers, 1963, 1969.
  • [9] F. Narita, Riemannian submersions and isometric reflections with respect to submanifolds, Math. J. Toyama Univ. 15 (1992), 83-94.
  • [10] F. Narita, Riemannian submersion with isometric reflections with respect to the fibers, Kodai Math. J. 16 (1993), 416-427.
  • [11] B. O'Neill, The fundamental equations of a submersion, Michigan Math. J. 13 (1966), 1-20.
  • [12] R. C. Randell, Generalized Brieskorn manifolds, Bull. Amer. Math. Soc. 80 (1974), 111-115.
  • [13] T. Takahashi, Deformations of Sasakian structures and its application to the Brieskorn manifolds, Tôhoku Math. J. 30 (1978), 37-43.
  • [14] Y. Tashiro, On contact structure of hypersurfaces in complex manifolds, I, ibid. 15 (1963), 62-78.
  • [15] I. Vaisman, On locally conformal almost Kähler manifolds, Israel J. Math. 24 (1976), 338-351.
  • [16] I. Vaisman, A theorem on compact locally conformal Kähler manifolds, Proc. Amer. Math. Soc. 75 (1979), 279-283.
  • [17] I. Vaisman, Locally conformal Kähler manifolds with parallel Lee form, Rend. Mat. 12 (1979), 263-284.
  • [18] I. Vaisman, Some curvature properties of locally conformal Kaehler manifolds, Trans. Amer. Math. Soc. (2) 259 (1980), 439-447.
  • [19] I. Vaisman, Generalized Hopf manifolds, Geom. Dedicata 13 (1982), 231-255.
  • [20] K. Yano and M. Kon, Generic submanifolds of Sasakian manifolds, Kodai Math. J. 3 (1980), 163-196.
  • [21] K. Yano and M. Kon, Structures on Manifolds, World Sci., Singapore, 1984.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-cmv70i2p165bwm
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