Generalized coKähler geometry and an application to generalized Kähler structures

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• 作者：Ralph R. Gomez ; ^{rgomez1@swarthmore.edu" class="auth_mail" title="E-mail the corresponding author} ; Janet Talvacchia
• 关键词：Generalized complex geometry ; Generalized contact geometry ; Cosymplectic ; CoKä ; hler
• 刊名：Journal of Geometry and Physics
• 出版年：2015
• 出版时间：December 2015
• 年：2015
• 卷：98
• 期：Complete
• 页码：493-503
• 全文大小：413 K

文摘

In this paper, we propose a generalization of classical coKähler geometry from the point of view of generalized contact metric geometry. This allows us to generalize a theorem of Capursi (1984), Goldberg (1968) and show that the product M₁×M₂$M_1\times M_2$ of generalized contact metric manifolds (M_i,Φ_i,E_±,i,G_i)$(M_i,{\Phi }_i,E_{\pm ,i},G_i)$, i=1,2$i=1,2$, where M₁×M₂$M_1\times M_2$ is endowed with the product (twisted) generalized complex structure induced from Φ₁${\Phi }_1$ and Φ₂${\Phi }_2$, is (twisted) generalized Kähler if and only if $(M_i,{\Phi }_i,E_{\pm ,i},G_i),i=1,2$ are (twisted) generalized coKähler structures. As an application of our theorem we construct new examples of twisted generalized Kähler structures on manifolds that do not admit a classical Kähler structure and we give examples of twisted generalized coKähler structures on manifolds which do not admit a classical coKähler structure.