2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/52890Using a method introduced by Hitchin we obtain the system of first order differential equations that determine the most general cohomogeniety one G_2 holonomy metric with S^3 \times S^3 principal orbits. The method is then applied to G_2 metric with S^3 \times T^3 principal orbits in which an analytic solution is obtained. The generalized metric has more free parameters than that previously constructed. After showing that the generalization is non-trivial a system of first order equations is obtained for new Spin(7) metric with principal orbits S^7.LaTex, 13 pagesHigh Energy Physics - Theorytext