2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/148803We investigate compact Kahler manifolds, which are acted on by a semisimple compact Lie group G of isometries with one hypersurface orbit. In case of ordinary action and projectable complex structure, we set up a one to one correspondence between such manifolds and abstract models. The Ricci tensor is then computed and we fully characterize the Kahler-Einstein manifolds with an ordinary cohomogeneity one action and projectable complex structure.29 pagesDifferential Geometry53C55 53C25 57S15text