2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/77364Let X be a compact Kaehler manifold. We expect that any direct sum decomposition of the tangent bundle T(X) comes from a splitting of the universal covering space of X as a product of manifolds, in such a way that the given decomposition of T(X) lifts to the canonical decomposition of the tangent bundle of a product. We prove this assertion when X is a Kaehler-Einstein manifold or a Kaehler surface. Simple examples show that the Kaehler hypothesis is necessary.9 pages, Plain TeX. We give a simpler proof of Theorem A following a paper of YauAlgebraic Geometrytext