Abstract
Starting from a real analytic surface ℳ with a real analytic conformal Cartan connection A. Bor´owka constructed a minitwistor space of an asymptotically hyperbolic Einstein–Weyl manifold with ℳ being the boundary. In this article, starting from a symmetry of conformal Cartan connection, we prove that symmetries of conformal Cartan connection on ℳ can be extended to symmetries of the obtained Einstein–Weyl manifold.
Highlights
A complex manifold M with a conformal structure [g] is a Weyl manifold if it is equipped with a holomorphic connection D that preserves [g]
Our final result is that under some mild conditions on the bundle appearing in the definition of the conformal Cartan connection, the symmetry we start with on the boundary M can be extended to a symmetry of the minitwistor space and it induces a symmetry of the corresponding Einstein–Weyl manifold
MC can be constructed by using holomorphic extensions of the real-analytic transition functions on M and the real structure will be given by the complex conjugation
Summary
A complex manifold M with a conformal structure [g] is a Weyl manifold if it is equipped with a holomorphic connection D that preserves [g]. Our final result is that under some mild conditions on the bundle appearing in the definition of the conformal Cartan connection, the symmetry we start with on the boundary M can be extended to a symmetry of the minitwistor space and it induces a symmetry of the corresponding Einstein–Weyl manifold. This result is analogous to the result in [1] where the c-projective symmetries under given conditions extend from the fixed points set of a circle action to quaternionic symmetries.
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