Dual Lefschetz Operator and Contraction with the Fundamental Form - MathOverflow most recent 30 from http://mathoverflow.net 2013-06-19T22:13:50Z http://mathoverflow.net/feeds/question/83638 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/83638/dual-lefschetz-operator-and-contraction-with-the-fundamental-form Dual Lefschetz Operator and Contraction with the Fundamental Form Ago Szekeres 2011-12-16T17:03:07Z 2011-12-16T17:03:07Z <p>Let $M$ be a Kahler manifold, with metric $g$, fundamental form $\omega$, and dual Lefschetz operator $\Lambda$. Now $\Lambda$, and contraction with $\omega$, both map the two forms $\Omega^2(M)$ to $0$-forms, ie smooth functions. Are they equal? I think this is almost certainly true, but I can't see a clean argument.</p> <p>Do I need Kahler here? I would guess this works for all complex manifolds.</p>