On a complex manifold an Hermitian metric which is simultaneously SKT and balanced has to be necessarily K\"ahler. It has been conjectured that if a compact complex manifold (M,J) has an SKT metric and a balanced metric both compatible with J, then (M, J) is necessarily K\"ahler. We show that the conjecture is true for nilmanifolds.
On the existence of balanced and SKT metrics on nilmanifolds
FINO, Anna Maria;VEZZONI, Luigi
2016-01-01
Abstract
On a complex manifold an Hermitian metric which is simultaneously SKT and balanced has to be necessarily K\"ahler. It has been conjectured that if a compact complex manifold (M,J) has an SKT metric and a balanced metric both compatible with J, then (M, J) is necessarily K\"ahler. We show that the conjecture is true for nilmanifolds.
File in questo prodotto:
Non ci sono file associati a questo prodotto.
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
