We study the Dirac spectrum on compact Riemannian spin manifolds $M$ equipped with a metric connection $abla$ with skew torsion $TinLambda^3M$ in the situation where the tangent bundle splits under the holonomy of $abla$ and the torsion of $abla$ is of `split' type. We prove an optimal lower bound for the first eigenvalue of the Dirac operator with torsion that generalizes Friedrich's classical Riemannian estimate.
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机译：我们研究了紧切的黎曼自旋流形$ M $配备公制连接$ nabla $并具有扭扭$ T in Lambda ^ 3M $的Dirac谱，其中正切束在$ nabla $的整平度下分裂$ nabla $的扭力是“分裂”类型的。我们证明了带扭转的Dirac算子的第一个特征值的最佳下界，该下界推广了Friedrich的经典Riemannian估计。
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