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arXiv · 2209.11301

The c-projective symmetry algebras of Kähler surfaces

Gianni Manno·Jan Schumm·Andreas Vollmer
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Abstract

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.

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Gianni Manno, Jan Schumm, Andreas Vollmer. 2024-12-06. The c-projective symmetry algebras of Kähler surfaces. https://doi.org/10.1007/s12220-024-01878-1

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