Secondary Chern-Euler class for general submanifold

TL;DR

This paper introduces the secondary Chern-Euler class for submanifolds in Riemannian geometry, enabling new insights into vector field indices with non-isolated singularities and providing conceptual proofs of classical results.

Contribution

It defines the secondary Chern-Euler class for general submanifolds and applies it to study vector field indices with non-isolated singularities.

Findings

Defined the secondary Chern-Euler class for submanifolds.

Developed a new approach to vector field indices with non-isolated singularities.

Provided conceptual proofs of classical results of Chern.

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.