The fourth-order mass of the product of 3-spheres

In this paper, we study the fourth-order mass related to the Q-curvature problem, which was introduced by Avalos, Laurain, and Lira recently. We derive explicit expressions and approximate values for the fourth-order mass of the product manifold S3×S3 and of its quotients SO(4) and RP3×RP3. This extends Viaclovsky’s results on the ADM masses [Arnowitt, R., Deser, S., and Misner, C. W., Phys. Rev. 122(3), 997–1006 (1961) and Geroch, R., J. Math. Phys. 13, 956–968 (1972)] of S2×S2, G(2, 4) and RP2×RP2.