The c-Projective Symmetry Algebras of Kähler Surfaces

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Let M be a Kähler manifold with complex structure J and Kähler metric g. A c-projective vector field is a vector field on M whose flow sends J-planar curves to J-planar curves, where J-planar curves are analogs of what (unparametrised) geodesics are for pseudo-Riemannian manifolds (without complex structure). The c-projective symmetry algebras of Kähler surfaces with essential (i.e., non-affine) c-projective vector fields are computed.