On Generalized Einstein Square Metrics

On Generalized Einstein Square Metrics

The class of generalized Einstein metrics are critical points of Hilbert integral in the sense of Akbar-Zadeh. In this paper, we characterize generalized Einstein square (a; b)-metric with isotropic S-curvature. We prove that this class of metrics has vanishing eR -curvature. Then, we show that every square metric of isotropic S-curvature and vanishing eR -curvature is R-quadratic. It results that every generalized Einstein square metric with isotropic S-curvature is R-quadratic