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We prove lower bounds for the eigenvalues of the Spinc Dirac operator on submanifolds. These estimates are expressed in terms of extrinsic and intrinsic quantities. We also give estimates involving the energy–momentum tensor as well as conformal bounds. The limiting cases of these estimates give rise to particular spinor fields, called generalized twisted Killing spinors, which are also studied.

Lower bounds for the eigenvalues of the Spin c Dirac operator on submanifolds