# zbMATH — the first resource for mathematics

Sur les droites privilégiées en un point d’une sous-variété V d’un espace euclidien et les directions principales des tubes autour de V. (On particular straight lines at a point of a submanifold V of a Euclidean space and the principal directions of tubes about V). (French) Zbl 0562.53002
Summary: One gives a geometrical interpretation of the index of relative nullity at the point $$x_ 0$$ of a submanifold V of a Euclidean space. Then one establishes relationships between the objects introduced in the author’s papers in Geom. Dedicata 12, 1-15 (1982; Zbl 0495.53003) and C. R. Acad. Sci., Paris, Ser. I 297, 651-654 (1983; Zbl 0533.53002) and the principal directions and centers of curvature of the tubes about V. Finally one studies the continuous determinations of the longitudinal principal directions of the tube along the curves in the spherical fiber over the point $$x_ 0$$ of V.

##### MSC:
 53A07 Higher-dimensional and -codimensional surfaces in Euclidean and related $$n$$-spaces
##### Keywords:
submanifold; curvature of the tubes; principal directions