Über die Riemannsche Einbettungsgeometrie der Veronesemannigfaltigkeiten

Abstract

Let E be a n-dimensional euclidean vector space. The subset V ⁿ_k ={x ⊗ ... ⊗ x | x ∈ E} of ⊗^kE is called a Veronesemanifold. The scalar product of E induces a euclidean structure on ⊗^kE. Passing to the corresponding projective space$\overline { \otimes ^k E}$, one may consider$\overline {V_k^n }$ as a riemannian submanifold of the space form$\overline { \otimes ^k E}$. In this paper we study properties of the pair$(\overline {V_k^n } , \overline { \otimes ^k E} )$ of riemannian manifolds.