AI 中文总结
本文基于Kodaira-Spencer理论，证明了由切丛或余切丛局部自由子层定义的叶状复解析结构形变的存在性与完备性定理，并推广至同时形变情形。
AI 中文摘要
我们基于Kodaira-Spencer的形变理论，研究了由切丛的局部自由子层和余切丛的局部自由子层定义的叶状复解析结构的形变。我们证明了由切丛的局部自由子层定义的叶状复解析结构的形变的存在性与完备性定理，作为Kodaira-Spencer关于复解析结构形变的存在性与完备性定理的类比。我们还证明了由余切丛的局部自由子层定义的叶状复解析结构的形变的存在性与完备性定理。此外，当紧致复流形上的奇异全纯叶状结构同时由切丛和余切丛的局部自由子层定义时，我们也证明了同时形变的存在性与完备性定理。
英文摘要
We study deformations of foliated complex analytic structures defined by locally free subsheaves of tangent sheaves and locally free subsheaves of cotangent sheaves on the basis of Kodaira-Spencer's deformation theory. We prove theorems of existence and completeness for deformations of foliated complex analytic structures defined by locally free subsheaves of tangent sheaves as analogues of theorems of existence and completeness for deformations of complex analytic structures by Kodaira-Spencer. We prove theorems of existence and completeness for deformations of foliated complex analytic structures defined by locally free subsheaves of cotangent sheaves. We also prove theorems of existence and completeness for simultaneous deformations when singular holomorphic foliations on compact complex manifolds are defined by locally free subsheaves of tangent and cotangent sheaves at the same time.
