Work

Compact Locally Conformally Pseudo-Kähler Manifolds with Essential Conformal Transformations

Year: 2024

Type: article

Abstract: A conformal transformation of a semi-Riemannian manifold is essential if there is no conformally equivalent metric for which it is an isometry. For Riemannian manifolds the existence of an essential conformal transformation forces the manifold to be conformally flat. This is false for pseudo-Riemannian manifolds, however compact examples of conformally curved manifolds with essential conformal transformation are scarce. Here we give examples of compact conformal manifolds in signature $(4n+2k,4n+2\ell)$ with essential conformal transformations that are locally conformally pseudo-Kähler and not conformally flat, where $n\ge 1$, $k, \ell \ge 0$. The corresponding local pseudo-Kähler metrics obtained by a local conformal rescaling are Ricci-flat.

Source: Symmetry Integrability and Geometry Methods and Applications

DOI: 10.3842/sigma.2024.084

Authors: Vicente Cortés, Thomas Leistner

Institution: The University of Adelaide

Language: English

Topic: Geometry and complex manifolds

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

Funders: Deutsche Forschungsgemeinschaft, Australian Research Council

Awards: Symmetry and geometric partial differential equations, G432818845, EXC 2121: Quantum Universe