Generalized geometry of Norden manifolds

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• 作者：Antonella Nannicini ; ^{antonella.nannicini@unifi.it" class="auth_mail" title="E-mail the corresponding author}
• 关键词：53C15 ; 53D18 ; 53C80 ; 53C38
• 刊名：Journal of Geometry and Physics
• 出版年：2016
• 出版时间：January 2016
• 年：2016
• 卷：99
• 期：Complete
• 页码：244-255
• 全文大小：418 K

文摘

Let (M,J,g,D)$(M,J,g,D)$ be a Norden manifold with the natural canonical connection D$D$ and let $\widehat{J}$ be the generalized complex structure on M$M$ defined by g$g$ and J$J$. We prove that $\widehat{J}$ is D$D$-integrable and we find conditions on the curvature of D$D$ under which the ±i$\pm i$-eigenbundles of $\widehat{J}$, $E_{\widehat{J}}^{1,0}$, 33ce4df2508611">$E_{\widehat{J}}^{0,1}$, are complex Lie algebroids. Moreover we proove that $E_{\widehat{J}}^{1,0}$ and ${\left(E_{\widehat{J}}^{1,0}\right)}^{\ast }$ are canonically isomorphic and this allow us to define the concept of generalized ${\overline{\partial }}_{\widehat{J}}$-operator of (M,J,g,D)$(M,J,g,D)$. Also we describe some generalized holomorphic sections. The class of Kähler–Norden manifolds plays an important role in this paper because for these manifolds $E_{\widehat{J}}^{1,0}$ and 33ce4df2508611">$E_{\widehat{J}}^{0,1}$ are complex Lie algebroids.