# zbMATH — the first resource for mathematics

Sur la courbure des sous-variétés d’un espace euclidien. (French) Zbl 0533.53002
Given a tangent vector v of a submanifold V of Euclidean space E, we take a curve c in V with initial vector v. Parallel transport in the tangent and normal bundle along c induces a local 1-parameter group of Euclidean motions. Its Killing vector field X on E depends only on v. The author studies X in relation to the curvatures of V and to the limits of intersections of tangent or normal spaces.
Reviewer: D.Ferus

##### MSC:
 53A07 Higher-dimensional and -codimensional surfaces in Euclidean and related $$n$$-spaces
##### Keywords:
submanifold; Parallel transport; Killing vector field