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
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.
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.