Conformal vector flelds on a Kahler manifold

For a 2n-dimensional Kahler manifold (M;J;g), using a con- formal transformation ' : M ! M, g = ' ⁄ g = e i2f g, we obtain a condi- tion under which (M;J;g) is a Kahler manifold and show that in general (M;J;g) is not a Kahler manifold. The Hermitian manifold (M;J;g) has a new structure which we call as Kahler-like manifold. We show that a Killing vector flelds on the Kahler manifold (M;J;g) are the conformal vector flelds on the Kahler-like manifold (M;J;g). Similarly it is shown that a Killing vector fleld on the Kahler-like manifold (M;J;g) is a con- formal vector fleld on the Kahler manifold (M;J;g).