Spectral geometry of eta-Einstein Sasakian manifolds

We extend a result of Patodi for closed Riemannian manifolds to the context of closed contact manifolds by showing the condition that a manifold is an $\eta$-Einstein Sasakian manifold is spectrally determined. We also prove that the condition that a Sasakian space form has constant $\phi$-sectional curvature $c$ is spectrally determined.