The Dirac operator on locally reducible Riemannian manifolds (Q2421284)

The article gives a lower bound for the (square of the) $N$-th eigenvalue of the Dirac operator on a locally reducible compact Riemannian spin manifold in terms of the minimum of the scalar curvature and the value of a smaller eigenvalue. This result extends the work by \textit{B. Alexandrov} [J. Geom. Phys. 57, No. 2, 467--472 (2007; Zbl 1116.58028)], which deals with the case $N=1$.