Timeline for Vanishing components of Kähler metric

4 events

when toggle format	what		by	license	comment
Jun 14, 2023 at 14:53	comment	added	Samir		Thank Michael, But i could not find any example such that $\partial \alpha^{n-1,n-2} \neq 0$
Jun 14, 2023 at 13:18	comment	added	Michael Albanese		If $n = 2$, then $\omega = d\alpha = \partial\alpha^{1,0} + (\bar{\partial}\alpha^{1,0} + \partial\alpha^{0,1}) + \bar{\partial}\alpha^{0,1}$. Given that $\omega$ has type $(1,1)$, we see that $\partial\alpha^{1,0} = 0$ and $\bar{\partial}\alpha^{0,1} = 0$. For $n > 2$, the same argument shows that $\partial\alpha^{n-1, n-2} + \bar{\partial}\alpha^{n, n-3} = 0$ and $\partial\alpha^{n-3, n} + \bar{\partial}\alpha^{n-2, n-1} = 0$.
Jun 13, 2023 at 20:14	history	edited	Samir	CC BY-SA 4.0	deleted 6 characters in body; edited tags
Jun 13, 2023 at 18:02	history	asked	Samir	CC BY-SA 4.0