Hard Lefschetz theorem for Vaisman manifolds
Cappelletti-Montano, Beniamino;De Nicola, Antonio;Yudin, Ivan
2019-01-01
Abstract
We establish a Hard Lefschetz Theorem for the de Rham cohomology of compact Vaisman manifolds. A similar result is proved for the basic cohomology with respect to the Lee vector field. Motivated by these results, we introduce the notions of a Lefschetz and of a basic Lefschetz locally conformal symplectic (l.c.s.) manifold of the first kind. We prove that the two notions are equivalent if there exists a Riemannian metric such that the Lee vector field is unitary and parallel and its metric dual 1-form coincides with the Lee 1-form. Finally, we discuss several examples of compact l.c.s. manifolds of the first kind which do not admit compatible Vaisman metrics.File | Dimensione | Formato | |
---|---|---|---|
HLT Vaisman.pdf Solo gestori archivio
Tipologia: versione pre-print
Dimensione 262.01 kB
Formato Adobe PDF
|
262.01 kB | Adobe PDF | Visualizza/Apri Richiedi una copia |
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.