We consider locally conformal Kaehler geometry as an equivariant, homothetic Kaehler geometry (K,Gamma). We show that the de Rham class of the Lee form can be naturally identified with the homomorphism projecting Gamma to its dilation factors, thus completing the description of locally conformal Kaehler geometry in this equivariant setting. The rank r of a locally conformal Kaehler manifold is the rank of the image of this homomorphism. Using algebraic number theory, we show that r is non-trivial, providing explicit examples of locally conformal Kaehler manifolds with r in {2,...,b_1-1}. As far as we know, these are the first examples of this kind. Moreover, we prove that locally conformal Kaehler Oeljeklaus-Toma manifolds have either r=b_1 or r=b_1/2.

Examples of non-trivial rank in locally conformal Kaehler geometry

PARTON, Maurizio
;
2012-01-01

Abstract

We consider locally conformal Kaehler geometry as an equivariant, homothetic Kaehler geometry (K,Gamma). We show that the de Rham class of the Lee form can be naturally identified with the homomorphism projecting Gamma to its dilation factors, thus completing the description of locally conformal Kaehler geometry in this equivariant setting. The rank r of a locally conformal Kaehler manifold is the rank of the image of this homomorphism. Using algebraic number theory, we show that r is non-trivial, providing explicit examples of locally conformal Kaehler manifolds with r in {2,...,b_1-1}. As far as we know, these are the first examples of this kind. Moreover, we prove that locally conformal Kaehler Oeljeklaus-Toma manifolds have either r=b_1 or r=b_1/2.
File in questo prodotto:
File Dimensione Formato  
pubblicato.pdf

accesso aperto

Tipologia: Documento in Post-print
Dimensione 178.8 kB
Formato Adobe PDF
178.8 kB Adobe PDF Visualizza/Apri

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11564/176846
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 17
  • ???jsp.display-item.citation.isi??? 19
social impact