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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2023
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2303.00631 |
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| _version_ | 1866910496098091008 |
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| author | He, Jie Zheng, Kai |
| author_facet | He, Jie Zheng, Kai |
| contents | Let $(M,ω)$ be a compact symplectic manifold. We denote by $\ac$ the space of all almost complex structure compatible with $ω$. $\ac$ has a natural foliation structure with the complexified orbit as leaf. We obtain an explicit formula of the Hessian of Hermitian Calabi functional at an extremal almost Kähler metric in $\ac$. We prove that the Hessian of Hermitian Calabi functional is semi-positive definite at critical point when restricted to a complexified orbit, as corollaries we obtain some results analogy to Kähler case. We also show weak parabolicity of the Hermitian Calabi flow. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2303_00631 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Hermitian Calabi functional in complexified orbits He, Jie Zheng, Kai Differential Geometry Let $(M,ω)$ be a compact symplectic manifold. We denote by $\ac$ the space of all almost complex structure compatible with $ω$. $\ac$ has a natural foliation structure with the complexified orbit as leaf. We obtain an explicit formula of the Hessian of Hermitian Calabi functional at an extremal almost Kähler metric in $\ac$. We prove that the Hessian of Hermitian Calabi functional is semi-positive definite at critical point when restricted to a complexified orbit, as corollaries we obtain some results analogy to Kähler case. We also show weak parabolicity of the Hermitian Calabi flow. |
| title | Hermitian Calabi functional in complexified orbits |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2303.00631 |