Abstract

In this paper, we construct two modified spinorial LeviCivita connection based on the EnergyMomentum tensor and its trace to bring an optimal lower bound to the eigenvalues of the compact Riemannian Spinsubmanifold Dirac operator in terms of the the EnergyMomentum tensor and its trace. Then, we extend these estimates in terms of the Yamabe number and the area of the submanifold under the conformal change of the metric.

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