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The Secondary Chern–Euler Class for a General Submanifold

Published online by Cambridge University Press:  20 November 2018

Zhaohu Nie*
Affiliation:
Department of Mathematics, Penn State Altoona, 3000 Ivyside Park, Altoona, PA 16601, USA e-mail: znie@psu.edu
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Abstract

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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.

Type
Research Article
Copyright
Copyright © Canadian Mathematical Society 2012

References

[1] Allendoerfer, C. B., The Euler number of a Riemann manifold. Amer. J. Math. 62(1940), 243248. http://dx.doi.org/10.2307/2371450 CrossRefGoogle Scholar
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[8] Sha, J.-P., A secondary Chern-Euler class. Ann. of Math. 150(1999), no. 3, 11511158. http://dx.doi.org/10.2307/121065 CrossRefGoogle Scholar
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