• Abdel-all, Nassar H. (Mathematics Department faculty of science Assiut University) ;
  • Hussein, Rawya A. (Mathematics Department Faculty of Science Assiut University)
  • Published : 1999.07.01


This work is concerned mainly with the variational problem on an immersion x:M $\rightarrow$} $E^4$ . 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.


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