*Published Paper*

**Inserted:** 14 dec 2001

**Last Updated:** 3 feb 2004

**Journal:** Ann. Mat. Pura ed Appl.

**Volume:** 182

**Number:** 3

**Pages:** 357-373

**Year:** 2003

**Abstract:**

The following result is proved: Let $M$ be a $n$-dimensional $C^1$-submanifold of $R^N$ which is domain of a given $\Lambda^n(R^N)$-valued map $\eta$ of class $C^1$. Then the subset of $M$ at points of which $\eta$ is nonzero, simple and tangent to $M$ is $C^2$ rectifiable. As a corollary we get a criterion for $C^2$-rectifiability of sets.

**Keywords:**
Rectifiable sets, C^2 rectifiability, sets with generalized curvature