TY - JOUR
T1 - Twisted Dirac operators and generalized gradients
AU - Homma, Yasushi
N1 - Funding Information:
This article was almost completed while the author stayed at Stuttgart University as a visiting researcher during his one year sabbatical. Thanks to all staffs of the institute of Geometry and Topology in Stuttgart University. Especially, the author is grateful to U. Semmelmann for his hospitality, fruitful discussions about spin geometry, and helpful comments to this article. The author also thanks D. Eelbode for a useful discussion about the twisted Dirac operator. This work was partially supported in part by JSPS KAKENHI Grant Number 15K04858.
Publisher Copyright:
© 2016, Springer Science+Business Media Dordrecht.
PY - 2016/9/1
Y1 - 2016/9/1
N2 - On Riemannian or spin manifolds, there are geometric first order differential operators called generalized gradients. In this article, we prove that the Dirac operator twisted with an associated bundle is a linear combination of some generalized gradients. This observation allows us to find all the homomorphism type Weitzenböck formulas. We also give some applications.
AB - On Riemannian or spin manifolds, there are geometric first order differential operators called generalized gradients. In this article, we prove that the Dirac operator twisted with an associated bundle is a linear combination of some generalized gradients. This observation allows us to find all the homomorphism type Weitzenböck formulas. We also give some applications.
KW - Dirac operator
KW - Generalized gradient
KW - Lichnerowicz Laplacian
KW - Weitzenböck formulas
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U2 - 10.1007/s10455-016-9503-7
DO - 10.1007/s10455-016-9503-7
M3 - Article
AN - SCOPUS:84960098941
SN - 0232-704X
VL - 50
SP - 101
EP - 127
JO - Annals of Global Analysis and Geometry
JF - Annals of Global Analysis and Geometry
IS - 2
ER -