International Journal of Mathematics and Mathematical Sciences
Volume 29 (2002), Issue 1, Pages 1-5

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

Copyright © 2002 Tarek Fathy Mersal and Mohamed Esmail Basher. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.