具有最终恒等式的$F$ -流形的Dubrovin对偶
Dubrovin's duality for $F$-manifolds with eventual identities
摘要：
F-流形（M，o，e）上的向量场E是最终恒等式，如果它是可逆的，并且乘法X*Y：= XoYoE ^{-1}定义了M上的一个新的F-流形结构。我们给这样的最终身份的一个特征，这是一个问题提出的Manin。我们开发了一个对偶的F-流形与最终的身份，我们表明，是兼容的局部不可约分解的F-流形，并保持类黎曼F-流形。我们发现充要条件的最终身份，确保谐波Higgs束和DChk结构被保存我们的对偶性。我们使用最终的身份来构造兼容的度量对。
英文摘要：
A vector field E on an F-manifold (M, o, e) is an eventual identity if it is invertible and the multiplication X*Y := X o Y o E^{-1} defines a new F-manifold structure on M. We give a characterization of such eventual identities, this being a problem raised by Manin. We develop a duality between F-manifolds with eventual identities and we show that is compatible with the local irreducible decomposition of F-manifolds and preserves the class of Riemannian F-manifolds. We find necessary and sufficient conditions on the eventual identity which insure that harmonic Higgs bundles and DChk-structures are preserved by our duality. We use eventual identities to construct compatible pair of metrics.
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