Tangent and normal bundles in almost complex geometry

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• 作者：Boris S. Kruglikov
• 关键词：Almost complex structure ; Normal bundle ; Nijenhuis tensor ; Minimal connection
• 刊名：Differential Geometry and its Applications
• 出版年：2007
• 出版时间：August 2007
• 年：2007
• 卷：25
• 期：4
• 页码：399-418
• 全文大小：297 K

文摘

We define and study pseudoholomorphic vector bundle structures, particular cases of which are tangent and normal bundle almost complex structures. As an application we deduce normal forms of almost complex structures along a pseudoholomorphic submanifold.

In dimension four we relate these normal forms to the problem of pseudoholomorphic foliation of a neighborhood of a curve and the question of non-deformation and persistence of pseudoholomorphic tori.