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

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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 
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     title = {Differential geometry of concircular submanifolds of {Euclidean} spaces},
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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/