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Transactions of the American Mathematical Society
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}$.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1990-0955489-4
PII: S 0002-9947(1990)0955489-4
Keywords: Flat surface, flat normal bundle, first normal space
Article copyright: © Copyright 1990 American Mathematical Society