C-projective symmetries of submanifolds in quaternionic geometry
| Authors | |
|---|---|
| Year of publication | 2019 |
| Type | Article in Periodical |
| Magazine / Source | Annals of Global Analysis and Geometry |
| MU Faculty or unit | |
| Citation | |
| Web | https://link.springer.com/article/10.1007/s10455-018-9631-3 |
| Doi | http://dx.doi.org/10.1007/s10455-018-9631-3 |
| Keywords | c-projective structure; Quaternionic structure; Symmetries; Submaximally symmetric spaces; Calabi metric |
| Description | The generalized Feix-Kaledin construction shows that c-projective 2n-manifolds with curvature of type (1,1) are precisely the submanifolds of quaternionic 4n-manifolds which are fixed-point set of a special type of quaternionic circle action. In this paper, we consider this construction in the presence of infinitesimal symmetries of the two geometries. First, we prove that the submaximally symmetric c-projective model with type (1,1) curvature is a submanifold of a submaximally symmetric quaternionic model and show how this fits into the construction. We give conditions for when the c-projective symmetries extend from the fixed-point set of the circle action to quaternionic symmetries, and we study the quaternionic symmetries of the Calabi and Eguchi-Hanson hyperkahler structures, showing that in some cases all quaternionic symmetries are obtained in this way. |
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