Curvature dependent lower bounds for the first eigenvalue of the Dirac operator

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Using Weitzenböck techniques on any compact Riemannian spin manifold we derive inequalities that involve a real parameter and join the eigenvalues of the Dirac operator with curvature terms. The discussion of these inequalities yields vanishing theorems for the kernel of the Dirac operator D and lower bounds for the spectrum of D² if the curvature satisfies certain conditions.