International Journal of Mathematics and Mathematical Sciences 
Volume 29 (2002), Issue 1, Pages 1-5
doi:10.1155/S016117120200666X

Super parallel immersions in Euclidean space

Tarek Fathy Mersal1 and Mohamed Esmail Basher2

 1Department of Mathematics, Faculty of Science, Menoufia University, Egypt
2Department of Mathematics, Faculty of Education (Suez), Suez Canal University, Egypt
Received 31 January 2001; Revised 20 May 2001

Abstract

Two submanifolds of Euclidean n-space En are called super parallel if the affine normal spaces are homothetic at the corresponding points. Characterizations are given for the action of conformal transformation on super parallel mates. Our notion is generalized to super transnormal submanifolds and its relation with super self-parallel submanifolds and convex super self-parallel submanifolds.