Eigenvalue estimates for multi-form modified Dirac operators

Jan Gutowski*, George Papadopoulos

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

7 Citations (Scopus)
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Abstract

We give estimates for the eigenvalues of multi-form modified Dirac operators which are constructed from a standard Dirac operator with the addition of a Clifford algebra element associated to a multi-degree form. In particular such estimates are presented for modified Dirac operators with a k-degree form 0≤k≤4, those modified with multi-degree (0,k)-form 0≤k≤3 and the horizon Dirac operators which are modified with a multi-degree (1,2,4)-form. In particular, we give the necessary geometric conditions for such operators to admit zero modes as well as those for the zero modes to be parallel with a respect to a suitable connection. We also demonstrate that manifolds which admit such parallel spinors are associated with twisted covariant form hierarchies which generalize the conformal Killing–Yano forms.

Original languageEnglish
Article number103954
Pages (from-to)1-
Number of pages24
JournalJOURNAL OF GEOMETRY AND PHYSICS
Volume160
Early online date1 Oct 2020
DOIs
Publication statusPublished - Feb 2021

Keywords

  • Differential geometry
  • Dirac equation

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