Geodesic
Differential geometry of concircular submanifolds of Euclidean spaces
Serdica Mathematical Journal, Tome 43 (2017) no. 1, pp. 035-048.

Voir la notice de l'article provenant de la source Bulgarian Digital Mathematics Library

A Euclidean submanifold is called a rectifying submanifold if its position vector field x always lies in its rectifying subspace [7]. It was proved in [7] that a Euclidean submanifold M is rectifying if and only if the tangential component x^T of its position vector field is a concurrent vector field.Since concircular vector fields are natural extension of concurrent vector fields, it is natural and fundamental to study a Euclidean submanifold M such that the tangential component x^T of the position vector field x of M is a concircular vector field. We simply call such a submanifold a concircular submanifold. The main purpose of this paper is to study concircular submanifolds in a Euclidean space. Our main result completely classifies concircular submanifolds in an arbitrary Euclidean space.
Keywords: Euclidean submanifold, position vector field, concurrent vector field, concircular vector field, rectifying submanifold, 53A07, 53C40, 53C42 
@article{SMJ2_2017_43_1_a2,
     author = {Chen, Bang-Yen and Walter Wei, Shihshu},
     title = {Differential geometry of concircular submanifolds of {Euclidean} spaces},
     journal = {Serdica Mathematical Journal},
     pages = {035--048},
     publisher = {mathdoc},
     volume = {43},
     number = {1},
     year = {2017},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SMJ2_2017_43_1_a2/}
}
TY  - JOUR
AU  - Chen, Bang-Yen
AU  - Walter Wei, Shihshu
TI  - Differential geometry of concircular submanifolds of Euclidean spaces
JO  - Serdica Mathematical Journal
PY  - 2017
SP  - 035
EP  - 048
VL  - 43
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SMJ2_2017_43_1_a2/
LA  - en
ID  - SMJ2_2017_43_1_a2
ER  - 
%0 Journal Article
%A Chen, Bang-Yen
%A Walter Wei, Shihshu
%T Differential geometry of concircular submanifolds of Euclidean spaces
%J Serdica Mathematical Journal
%D 2017
%P 035-048
%V 43
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SMJ2_2017_43_1_a2/
%G en
%F SMJ2_2017_43_1_a2
Chen, Bang-Yen; Walter Wei, Shihshu. Differential geometry of concircular submanifolds of Euclidean spaces. Serdica Mathematical Journal, Tome 43 (2017) no. 1, pp. 035-048. http://geodesic.mathdoc.fr/item/SMJ2_2017_43_1_a2/