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- W4378575847 abstract "We revisit construction of the Atiyah-Hitchin manifold in the generalized Legendre transform approach. This is originally studied by Ivanov and Rocek and is subsequently investigated more by Ionas, in the latter of which the explicit forms of the Kahler potential and the Kahler metric are calculated. There is a difference between the former and the latter. In the generalized Legendre transform approach, a Kahler potential is constructed from the contour integration of one function with holomorphic coordinates. The choice of the contour in the latter is different from the former's one, whose difference may yield a discrepancy in the Kahler potential and eventually in the Kahler metric. We show that the former only gives the real Kahler potential, which is consistent with its definition, while the latter yields the complex one. We derive the Kahler potential and the metric for the Atiyah-Hitchin manifold in terms of holomorphic coordinates for the contour considered by Ivanov and Rov{c}ek for the first time." @default.
- W4378575847 created "2023-05-28" @default.
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- W4378575847 date "2023-05-27" @default.
- W4378575847 modified "2023-09-26" @default.
- W4378575847 title "Revisiting Atiyah–Hitchin manifold in the generalized Legendre transform" @default.
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- W4378575847 doi "https://doi.org/10.1093/ptep/ptad066" @default.
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