On Frenet frames of complex submanifolds in complex projective spaces (Q1069004)

The main results of this paper concern the curvature of a certain osculating bundle of complex projective manifolds. The author obtains a formula which generalizes a formula by Weyl for holomorphic curves - a so-called unintegrated Plücker formula. As a corollary he obtains the following characterization: The Veronese surfaces is the only surface in \({\mathbb{P}}^ 5\) whose second order osculating spaces all have the maximal dimension 5. This result has been generalized to a characterization of n-fold Veronese embeddings \({\mathbb{P}}^ r\to {\mathbb{P}}^ N,\) \(N=\left( \begin{matrix} n+r\\ r\end{matrix} \right)-1,\) by the author, \textit{W. Fulton}, \textit{S. Kleiman}, and the reviewer in Bull. Soc. Math. Fr. 113, 205-210 (1985).