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arXiv · 1208.2031

Twistorial eigenvalue estimates for generalized Dirac operators with torsion

Ilka Agricola·Julia Becker-Bender·Hwajeong Kim
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Abstract

We study the Dirac spectrum on compact Riemannian spin manifolds $M$ equipped with a metric connection $\nabla$ with skew torsion $T\in\Lambda^3M$ by means of twistor theory. An optimal lower bound for the first eigenvalue of the Dirac operator with torsion is found that generalizes Friedrich's classical Riemannian estimate. We also determine a novel twistor and Killing equation with torsion and use it to discuss the case in which the minimum is attained in the bound.

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Ilka Agricola, Julia Becker-Bender, Hwajeong Kim. 2012-08-09. Twistorial eigenvalue estimates for generalized Dirac operators with torsion. https://arxiv.org/abs/1208.2031

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