Lower bounds for the eigenvalue estimates of the submanifold Dirac operator

作者：Chen, Yongfa^*

来源：Mathematische Zeitschrift, 2021, 299(3-4): 2443-2460.

DOI：10.1007/s00209-021-02752-4

• Dirac operator
• Eigenvalue
• Mean curvature
• Scalar curvature

We get optimal lower bounds for the eigenvalues of the submanifold Dirac operator on locally reducible Riemannian manifolds in terms of intrinsic and extrinsic expressions. The limiting-cases are also studied. As a corollary, we can recover several known results in this direction.