Journal of the
Korean Mathematical Society JKMS

Using the results in the paper [12], we give an estimate for the first positive and negative Dirac eigenvalue on a 7-dimensional Sasakian spin manifold. The limiting case of this estimate can be attained if the manifold under consideration admits a Sasakian Killing spinor. By imposing the eta-Einstein condition on Sasakian manifolds of higher dimensions $2m+1 \geq 9$, we derive some new Dirac eigenvalue inequalities that improve the recent results in [12, 13].

Keywords: Dirac operator, first eigenvalue, Sasakian manifold

MSC numbers: 53C25, 53C27