Twisted Dirac operators and generalized gradients

Yasushi Homma*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

4 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)101-127
Number of pages27
JournalAnnals of Global Analysis and Geometry
Issue number2
Publication statusPublished - 2016 Sept 1


  • Dirac operator
  • Generalized gradient
  • Lichnerowicz Laplacian
  • Weitzenböck formulas

ASJC Scopus subject areas

  • Analysis
  • Political Science and International Relations
  • Geometry and Topology


Dive into the research topics of 'Twisted Dirac operators and generalized gradients'. Together they form a unique fingerprint.

Cite this