Geodesic
The Secondary Chern–Euler Class for a General Submanifold
Canadian mathematical bulletin, Tome 55 (2012) no. 2, pp. 368-377

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DOI

We define and study the secondary Chern–Euler class for a general submanifold of a Riemannian manifold. Using this class, we define and study the index for a vector field with non-isolated singularities on a submanifold. As an application, we give conceptual proofs of a result of Chern.
DOI : 10.4153/CMB-2011-077-8
Mots-clés : 57R20, secondary Chern–Euler class, normal sphere bundle, Euler characteristic, index, nonisolated singularities, blow-up 
Nie, Zhaohu. The Secondary Chern–Euler Class for a General Submanifold. Canadian mathematical bulletin, Tome 55 (2012) no. 2, pp. 368-377. doi: 10.4153/CMB-2011-077-8
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     author = {Nie, Zhaohu},
     title = {The {Secondary} {Chern{\textendash}Euler} {Class} for a {General} {Submanifold}},
     journal = {Canadian mathematical bulletin},
     pages = {368--377},
     year = {2012},
     volume = {55},
     number = {2},
     doi = {10.4153/CMB-2011-077-8},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2011-077-8/}
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