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1993 | 64 | 2 | 203-214
Tytuł artykułu

On normal CR-submanifolds of S-manifolds

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
Many authors have studied the geometry of submanifolds of Kaehlerian and Sasakian manifolds. On the other hand, David E. Blair has initiated the study of S-manifolds, which reduce, in particular cases, to Sasakian manifolds ([1, 2]). I. Mihai ([8]) and L. Ornea ([9]) have investigated CR-submanifolds of S-manifolds. The purpose of the present paper is to study a special kind of such submanifolds, namely the normal CR-submanifolds. In Sections 1 and 2, we review basic formulas and definitions for submanifolds in Riemannian manifolds and in S-manifolds, respectively, which we shall use later. In Section 3, we introduce normal CR-submanifolds of S-manifolds and we study some properties of their geometry. Finally, in Section 4, we consider those submanifolds in the case of the ambient S-manifold being an S-space form.
Słowa kluczowe
Rocznik
Tom
64
Numer
2
Strony
203-214
Opis fizyczny
Daty
wydano
1993
otrzymano
1991-12-02
Twórcy
  • Dpto. Algebra, Computación, Geometría Y Topologíai, Facultad de Matemáticas, Universidad de Sevilla, Apdo. Correos 1160, 41080 Sevilla, Spain
  • Dpto. Algebra, Computación, Geometría Y Topologíai, Facultad de Matemáticas, Universidad de Sevilla, Apdo. Correos 1160, 41080 Sevilla, Spain
  • Dpto. Algebra, Computación, Geometría Y Topologíai, Facultad de Matemáticas, Universidad de Sevilla, Apdo. Correos 1160, 41080 Sevilla, Spain
Bibliografia
  • [1] D. E. Blair, Geometry of manifolds with structural group U(n)×O(s), J. Differential Geom. 4 (1970), 155-167.
  • [2] D. E. Blair, On a generalization of the Hopf fibration, Ann. Ştiinţ. Univ. 'Al. I. Cuza' Iaşi 17 (1) (1971), 171-177.
  • [3] D. E. Blair, G. D. Ludden and K. Yano, Differential geometric structures on principal toroidal bundles, Trans. Amer. Math. Soc. 181 (1973), 175-184.
  • [4] J. L. Cabrerizo, L. M. Fernández and M. Fernández, A classification of totally f-umbilical submanifolds of an S-manifold, Soochow J. Math. 18 (2) (1992), 211-221.
  • [5] L. M. Fernández, CR-products of S-manifolds, Portugal. Mat. 47 (2) (1990), 167-181.
  • [6] I. Hasegawa, Y. Okuyama and T. Abe, On p-th Sasakian manifolds, J. Hokkaido Univ. Ed. Sect. II A 37 (1) (1986), 1-16.
  • [7] M. Kobayashi and S. Tsuchiya, Invariant submanifolds of an f-manifold with complemented frames, Kodai Math. Sem. Rep. 24 (1972), 430-450.
  • [8] I. Mihai, CR-subvarietăţi ale unei f-varietăţi cu repere complementare, Stud. Cerc. Mat. 35 (2) (1983), 127-136.
  • [9] L. Ornea, Subvarietăţi Cauchy-Riemann generice în S-varietăţi, ibid. 36 (5) (1984), 435-443.
  • [10] K. Yano, On a structure defined by a tensor fie1ld f of type (1,1) satisfying $f^3+f=0$, Tensor 14 (1963), 99-109.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-cmv64i2p203bwm
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