Self-similar Hessian and conformally Kahler manifolds

A self-similar Hessian (special Kahler) manifold is a Hessian (special Kahler) manifold (M, del, g) endowed with an affine (holomorphic) homothetic vector field xi. Consider an action of a group G on a self-similar Hessian (special Kahler) manifold (M, del, g, xi) by affine (holomorphic) isometrics preserving xi such that G acts on the level set {g(xi, xi) = 1} simply transitively. Then, we construct a homogeneous conformally Kahler (hyper Kahler) structure on TM (T*M).

Automated summary

This article discusses self-similar Hessian (special Kahler) manifolds and their actions with a group. It also introduces the construction of a conformally Kahler (hyper Kahler) structure on TM (T*M).