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<p>Let <i>M</i> be a Kähler manifold with complex structure <i>J</i> and Kähler metric <i>g</i>. A c-projective vector field is a vector field on <i>M</i> whose flow sends <i>J</i>-planar curves to <i>J</i>-planar curves, where <i>J</i>-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.</p>

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The c-Projective Symmetry Algebras of Kähler Surfaces

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年2月6日

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  • G. Manno,
  • J. Schumm,
  • A. Vollmer

摘要

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.