On normal CR-submanifolds of S-manifolds

• Autorzy: José L. Cabrerizo , Luis M. Fernández , Manuel Fernández
• 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

EN

S-manifolds; normal CR-submanifolds; S-space forms

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 1993
• Tom: 64
• Numer: 2
• Strony: 203-214

Daty

wydano

1993

otrzymano

1991-12-02

Twórcy

autor

José L. Cabrerizo

• Dpto. Algebra, Computación, Geometría Y Topologíai, Facultad de Matemáticas, Universidad de Sevilla, Apdo. Correos 1160, 41080 Sevilla, Spain

autor

Luis M. Fernández

• Dpto. Algebra, Computación, Geometría Y Topologíai, Facultad de Matemáticas, Universidad de Sevilla, Apdo. Correos 1160, 41080 Sevilla, Spain

autor

Manuel Fernández

• 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.