Eta-Einstein S-Manifolds and Spectral Geometry

We examine the spectral geometry of η-Einstein S-manifolds and compute the the spectral coefficients for S-space form and obtain the results analogue to Patodi’s results for Riemannian manifolds and J. Park results for η−Einstein Sasakian manifolds. We show that how an η−Einstein S-manifold and S-space forms are spectrally determined.