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Korean Mathematical Society JKMS

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J. Korean Math. Soc. 1999; 36(4): 663-677

Printed July 1, 1999

Copyright © The Korean Mathematical Society.

On the stability of immersed manifolds in $E^4$

Nassar H. Abdel-All, and Rawya A. Hussein

Abstract

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This work is concerned mainly with the variational problem on an immersion $x: M\to E^{4}$. A new approach is introduced depends on the normal variation in any arbitrary normal direction in the normal bundle. The results of this work are considered as a continuation and an extension to that obtained in [1], [2] and [3], [4] respectively. The methods adapted here are based on Cartan's methods of moving frames and the calculus of variations.

Keywords: stability, immersion, normal variation

MSC numbers: 53A10, 53B25, 53C40, 53C45

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