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1991 | 62 | 2 | 293-297
Tytuł artykułu

On K-contact Riemannian manifolds with vanishing E-contact Bochner curvature tensor

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
For Sasakian manifolds, Matsumoto and Chūman [6] defined the contact Bochner curvature tensor (see also Yano [9]). Hasegawa and Nakane [4] and Ikawa and Kon [5] have studied Sasakian manifolds with vanishing contact Bochner curvature tensor. Such manifolds were studied in the theory of submanifolds by Yano ([9] and [10]). In this paper we define an extended contact Bochner curvature tensor in K-contact Riemannian manifolds and call it the E-contact Bochner curvature tensor. Then we show that a K-contact Riemannian manifold with vanishing E-contact Bochner curvature tensor is a Sasakian manifold.
Słowa kluczowe
Rocznik
Tom
62
Numer
2
Strony
293-297
Opis fizyczny
Daty
wydano
1991
otrzymano
1989-10-18
poprawiono
1990-07-30
Twórcy
autor
  • Kohnodai Senior High School, 2-4-1, Kohnodai, Ichikawa-Shi, Chiba-Ken, 272 Japan
Bibliografia
  • [1] D. E. Blair, On the non-existence of flat contact metric structures, Tôhoku Math. J. 28 (1976), 373-379.
  • [2] D. E. Blair, Two remarks on contact metric structures, ibid. 29 (1977), 319-324.
  • [3] H. Endo, Invariant submanifolds in a K-contact Riemannian manifold, Tensor (N.S.) 28 (1974), 154-156.
  • [4] I. Hasegawa and T. Nakane, On Sasakian manifolds with vanishing contact Bochner curvature tensor II, Hokkaido Math. J. 11 (1982), 44-51.
  • [5] T. Ikawa and M. Kon, Sasakian manifolds with vanishing contact Bochner curvature tensor and constant scalar curvature, Colloq. Math. 37 (1977), 113-122.
  • [6] M. Matsumoto and G. Chūman, On the C-Bochner tensor, TRU Math. 5 (1969), 21-30.
  • [7] Z. Olszak, On contact metric manifolds, Tôhoku Math. J. 31 (1979), 247-253.
  • [8] S. Tanno, The topology of contact Riemannian manifolds, Illinois J. Math. 12 (1968), 700-712.
  • [9] K. Yano, Anti-invariant submanifolds of a Sasakian manifold with vanishing contact Bochner curvature tensor, J. Differential Geom. 12 (1977), 153-170.
  • [10] K. Yano, Differential geometry of anti-invariant submanifolds of a Sasakian manifold, Boll. Un. Mat. Ital. 12 (1975), 279-296.
  • [11] K. Yano and M. Kon, Structures on Manifolds, World Scientific, Singapore 1984.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-cmv62i2p293bwm
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