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François G. Dorais
François G. Dorais
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pull back of a K\"{a}hlerKähler form by a smooth circle group action on a compact K\"{a}hlerKähler manifold

Suppose a compact K"{a}hlerKähler manifold $(M,\omega)$ admits a smooth circle action $g_t,~t\in S^1$. So the pull back of the K"{a}hlerKähler form $g_t^{\ast}(\omega)$ is a nondegenerate two-form. Since the circle action is only smooth and may not preserve the complex structure, $g_t^{\ast}(\omega)$ may not be $(1,1)$-from. My question is if it is possible for some special manifolds or under some special cases $g_t^{\ast}(\omega)$ is $(1,1)$ for any $t$.

pull back of a K\"{a}hler form by a smooth circle group action on a compact K\"{a}hler manifold

Suppose a compact K"{a}hler manifold $(M,\omega)$ admits a smooth circle action $g_t,~t\in S^1$. So the pull back of the K"{a}hler form $g_t^{\ast}(\omega)$ is a nondegenerate two-form. Since the circle action is only smooth and may not preserve the complex structure, $g_t^{\ast}(\omega)$ may not be $(1,1)$-from. My question is if it is possible for some special manifolds or under some special cases $g_t^{\ast}(\omega)$ is $(1,1)$ for any $t$.

pull back of a Kähler form by a smooth circle group action on a compact Kähler manifold

Suppose a compact Kähler manifold $(M,\omega)$ admits a smooth circle action $g_t,~t\in S^1$. So the pull back of the Kähler form $g_t^{\ast}(\omega)$ is a nondegenerate two-form. Since the circle action is only smooth and may not preserve the complex structure, $g_t^{\ast}(\omega)$ may not be $(1,1)$-from. My question is if it is possible for some special manifolds or under some special cases $g_t^{\ast}(\omega)$ is $(1,1)$ for any $t$.

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Kevin
Kevin
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pull back of a K\"{a}hler form by a smooth circle group action on a compact K\"{a}hler manifold

Suppose a compact K"{a}hler manifold $(M,\omega)$ admits a smooth circle action $g_t,~t\in S^1$. So the pull back of the K"{a}hler form $g_t^{\ast}(\omega)$ is a nondegenerate two-form. Since the circle action is only smooth and may not preserve the complex structure, $g_t^{\ast}(\omega)$ may not be $(1,1)$-from. My question is if it is possible for some special manifolds or under some special cases $g_t^{\ast}(\omega)$ is $(1,1)$ for any $t$.