2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/67088In this paper an analytic proof of a generalization of a theorem of Bismut ([Bis1, Theorem 5.1]) is given, which says that, when $v$ is a transversal holomorphic vector field on a compact complex manifold $X$ with a zero point set $Y$, the embedding $j:Y\to X$ induces a natural isomorphism between the holomorphic equivariant cohomology of $X$ via $v$ with coefficients in $ξ$ and the Dolbeault cohomology of $Y$ with coefficients in $ξ|_Y$, where $ξ\to X$ is a holomorphic vector bundle over $X$.18 pages. has been accepted by International Journal of MathematicsDifferential GeometryMathematical PhysicsSpectral Theory53C; 58Jtext