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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Surfaces of $ E\sp 4$ satisfying certain restrictions on their normal bundle

Authors: Th. Hasanis, D. Koutroufiotis and P. Pamfilos
Journal: Trans. Amer. Math. Soc. 319 (1990), 329-347
MSC: Primary 53A07; Secondary 53C45
MathSciNet review: 955489
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Abstract: We consider smooth surfaces in $ {E^4}$ whose normal bundles satisfy certain geometric conditions that entail the vanishing of the normal curvature, and prove that their Gauss curvatures cannot be bounded from above by a negative number. We also give some results towards a classification of flat surfaces with flat normal bundle in $ {E^4}$.

References [Enhancements On Off] (What's this?)

  • [1] S. S. Chern, La géométrie des sous-variétés d'un espace euclidien à plusieurs dimensions, Enseign. Math. 40 (1951-54), 26-46. MR 0068280 (16:856g)
  • [2] Th. Hasanis and D. Koutroufiotis, Applications of the Gauss mapping for hypersurfaces of the sphere, Lecture Notes in Math., vol. 1156, Springer-Verlag, pp. 180-193. MR 824066 (88e:53080)
  • [3] L. Rodriguez and R. Tribuzy, Reduction of codimension of regular immersions, Math. Z. 18 (1984), 321-331. MR 731680 (85b:53065)

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Keywords: Flat surface, flat normal bundle, first normal space
Article copyright: © Copyright 1990 American Mathematical Society

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