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Product submanifolds with pointwise 3-planar normal sections

Published online by Cambridge University Press:  18 May 2009

Kadri Arslan  and
Alan West
Kadri Arslan
Affiliation:
Uludağ Universitesi; Fen-Edebiyat Fakültesi, Matematik Bölümü, Görükle Kampüsü, Bursa, Turkey
Alan West
Affiliation:
Department of Pure Mathematics, the University of LeedsLeeds, LS2 9JT, England
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Let M be a smooth m-dimensional submanifold in (m + d)-dimensional Euclidean space ℝm+d For x ∊ M and a non-zero vector X in TXM, we define the (d + l)-dimensional affine subspace E(x, X) ofℝm+d by

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 37 , Issue 1 , January 1995 , pp. 73 - 81
Copyright
Copyright © Glasgow Mathematical Journal Trust 1995

References

REFERENCES

1.Arslan, K. and West, A., Non-spherical submanifolds with pointwise 2-planar normal sections. Bull. London Math. Soc. (to appear).Google Scholar
2.Chen, B.-Y., Geometry of Submanifolds, (Dekker, 1973).Google Scholar
3.Chen, B. Y., Differential geometry of submanifolds with planar normal sections, Ann. Math. Pure Appl., 130 (1982), 59–66.CrossRefGoogle Scholar
4.Deprez, J. and Verstraelen, P., Immersions with circular normal sections and normal sections of product immersions Geom. Dedicala 20 (1986), 335–344.Google Scholar
5.Ferrus, D., Symmetric submanifolds of Euclidean space, Math. Ann. 247 (1980), 81–93.CrossRefGoogle Scholar
6.Li, S. J., Isotropic submanifolds with pointwise 3-planar normal sections, Boll. Un. Mat. Ital. (7) 1-B (1987), 373–385.Google Scholar
7.Li, S. J., Spherical submanifolds with pointwise 3 or 4-planar normal sections, Yokohama Math. J. 35 (1987), 21–31.Google Scholar
8.Moore, D., Isometric immersions of Riemannian products, J. Diff. Geom. 5 (1971), 159–168.Google Scholar