Secondary Chern-Euler class for general submanifold

Abstract

We define and study the secondary Chern-Euler class for a general submanifold of a Riemannian manifold. Using this class, we define and study index for a vector field with non-isolated singularities on a submanifold. As an application, our studies give conceptual proofs of a classical result of Chern.

Section 2 expanded and fixed. Final version to appear in Canadian Mathematical Bulletin