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
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.