Local Classification of Conformally-Einstein Kähler Metrics in Higher Dimensions

• Autores: Andrzej Derdzinski
• Localización: Proceedings of the London Mathematical Society, ISSN 0024-6115, Vol. 87, Nº 3, 2003, págs. 779-819
• Idioma: inglés
• DOI: 10.1112/s0024611503014175
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• Resumen

  • The requirement that a (non-Einstein) Kähler metric in any given complex dimension $m > 2$ be almost-everywhere conformally Einstein turns out to be much more restrictive, even locally, than in the case of complex surfaces. The local biholomorphic-isometry types of such metrics depend, for each $m > 2$, on three real parameters along with an arbitrary Kähler¿Einstein metric $h$ in complex dimension $m - 1$. We provide an explicit description of all these local-isometry types, for any given $h$. This result is derived from a more general local classification theorem for metrics admitting functions that we call special Kähler¿Ricci potentials.