A classification of certain submanifolds of an S-manifold

José L. Cabrerizo; Luis M. Fernández; Manuel Fernández

Annales Polonici Mathematici (1991)

  • Volume: 54, Issue: 2, page 117-123
  • ISSN: 0066-2216

Abstract

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A classification theorem is obtained for submanifolds with parallel second fundamental form of an 𝑆-manifold whose invariant f-sectional curvature is constant.

How to cite

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José L. Cabrerizo, Luis M. Fernández, and Manuel Fernández. "A classification of certain submanifolds of an S-manifold." Annales Polonici Mathematici 54.2 (1991): 117-123. <http://eudml.org/doc/262437>.

@article{JoséL1991,
abstract = {A classification theorem is obtained for submanifolds with parallel second fundamental form of an 𝑆-manifold whose invariant f-sectional curvature is constant.},
author = {José L. Cabrerizo, Luis M. Fernández, Manuel Fernández},
journal = {Annales Polonici Mathematici},
keywords = {𝑆-manifolds; parallel second fundamental form; S-manifolds; f-structures; polynomial structure},
language = {eng},
number = {2},
pages = {117-123},
title = {A classification of certain submanifolds of an S-manifold},
url = {http://eudml.org/doc/262437},
volume = {54},
year = {1991},
}

TY - JOUR
AU - José L. Cabrerizo
AU - Luis M. Fernández
AU - Manuel Fernández
TI - A classification of certain submanifolds of an S-manifold
JO - Annales Polonici Mathematici
PY - 1991
VL - 54
IS - 2
SP - 117
EP - 123
AB - A classification theorem is obtained for submanifolds with parallel second fundamental form of an 𝑆-manifold whose invariant f-sectional curvature is constant.
LA - eng
KW - 𝑆-manifolds; parallel second fundamental form; S-manifolds; f-structures; polynomial structure
UR - http://eudml.org/doc/262437
ER -

References

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  1. [1] D. E. Blair, Geometry of manifolds with structural group U(n) × O(s), J. Differential Geom. 4 (1970), 155-167. Zbl0202.20903
  2. [2] D. E. Blair, On a generalization of the Hopf fibration, An. Ştiinţ Univ. 'Al. I. Cuza' Iaşi 17 (1) (1971), 171-177. 
  3. [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. Zbl0276.53026
  4. [4] J. Erbacher, Reduction of the codimension of an isometric immersion, J. Differential Geom. 5 (1971), 333-340. Zbl0221.53031
  5. [5] I. Hasegawa, Y. Okuyama and T. Abe, On p-th Sasakian manifolds, J. Hokkaido Univ. Ed. Sect. II A 37 (1) (1986), 1-16. 
  6. [6] M. Kobayashi and S. Tsuchiya, Invariant submanifolds of an f-manifold with complemented frames, Kôdai Math. Sem. Rep. 24 (1972), 430-450. Zbl0246.53038
  7. [7] S. Tanno, Sasakian manifolds with constant ψ-holomorphic sectional curvature, Tôhoku Math. J. 21 (1969), 501-507. Zbl0188.26801
  8. [8] K. Yano, On a structure defined by a tensor field f of type (1,1) satisfying f³ + f = 0, Tensor 14 (1963), 99-109. Zbl0122.40705

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