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Michael Albanese
Michael Albanese
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For a compact Kähler manifold, we say that a form is primitive if it is contaned in the kernel of the dual Lefschetz operator, or the co-Lefschetz operator. For all examples I know, a primitive form $\omega$ is closed with respect to the $d$ de Rham exterior derivative if and only if $\omega$ is harmonic. I suspect that this is true for any compact Kähler manifold, but I don;tdon't know how one would prove it.

For a compact Kähler manifold, we say that a form is primitive if it is contaned in the kernel of the dual Lefschetz operator, or the co-Lefschetz operator. For all examples I know, a primitive form $\omega$ is closed with respect to the $d$ de Rham exterior derivative if and only if $\omega$ is harmonic. I suspect that this is true for any compact Kähler manifold, but I don;t know how one would prove it.

For a compact Kähler manifold, we say that a form is primitive if it is contaned in the kernel of the dual Lefschetz operator, or the co-Lefschetz operator. For all examples I know, a primitive form $\omega$ is closed with respect to the $d$ de Rham exterior derivative if and only if $\omega$ is harmonic. I suspect that this is true for any compact Kähler manifold, but I don't know how one would prove it.

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Michael Albanese
Michael Albanese
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de Rham closed harmonic form on a KaehlerKähler manifold

For a compact KahlerKähler manifold, we say that a form is primitive if it is contaned in the kernel of the dual Lefschetz operator, or the co-Lefschetz operator. For all examples I know, a primitive form $\omega$ is closed with respect to the d$d$ de Rham exterior derivative if and only if $\omega$ is harmonic. I suspect that this is true for any compact K"ahlerKähler manifold, but I don;t know how one would prove it.

de Rham closed harmonic form on a Kaehler manifold

For a compact Kahler manifold, we say that a form is primitive if it is contaned in the kernel of the dual Lefschetz operator, or the co-Lefschetz operator. For all examples I know, a primitive form $\omega$ is closed with respect to the d de Rham exterior derivative if and only if $\omega$ is harmonic. I suspect that this is true for any compact K"ahler manifold, but I don;t know how one would prove it.

de Rham closed harmonic form on a Kähler manifold

For a compact Kähler manifold, we say that a form is primitive if it is contaned in the kernel of the dual Lefschetz operator, or the co-Lefschetz operator. For all examples I know, a primitive form $\omega$ is closed with respect to the $d$ de Rham exterior derivative if and only if $\omega$ is harmonic. I suspect that this is true for any compact Kähler manifold, but I don;t know how one would prove it.

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Lars Pettersen
Lars Pettersen
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de Rham closed harmonic form on a Kaehler manifold

For a compact Kahler manifold, we say that a form is primitive if it is contaned in the kernel of the dual Lefschetz operator, or the co-Lefschetz operator. For all examples I know, a primitive form $\omega$ is closed with respect to the d de Rham exterior derivative if and only if $\omega$ is harmonic. I suspect that this is true for any compact K"ahler manifold, but I don;t know how one would prove it.