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arXiv · 1911.02281

Eigenvalue estimates for multi-form modified Dirac operators

J. Gutowski·G. Papadopoulos
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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 $0\leq k\leq 4$, those modified with multi-degree $(0,k)$-form $0\leq k\leq 3$ 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.

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J. Gutowski, G. Papadopoulos. 2019-11-06. Eigenvalue estimates for multi-form modified Dirac operators. https://arxiv.org/abs/1911.02281

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