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- 저자 : Giuseppe Tomassini (검색결과 2 건)
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COMPLEX SUBMANIFOLDS IN REAL HYPERSURFACES
한종규,Giuseppe Tomassini 대한수학회 2010 대한수학회지 Vol.47 No.5
Let M be a C∞ real hypersurface in Cn+1, n ¸ 1, locally given as the zero locus of a C∞ real valued function r that is defined on a neighborhood of the reference point P ∈ M. For each k = 1, . . . , n we present a necessary and sufficient condition for there to exist a complex manifold of dimension k through P that is contained in M, assuming the Levi form has rank n − k at P. The problem is to find an integral manifold of the real 1-form i□r on M whose tangent bundle is invariant under the complex structure tensor J. We present generalized versions of the Frobenius theorem and make use of them to prove the existence of complex submanifolds.
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COMPLEX SUBMANIFOLDS IN REAL HYPERSURFACES
Han, Chong-Kyu,Tomassini, Giuseppe Korean Mathematical Society 2010 대한수학회지 Vol.47 No.5
Let M be a $C^{\infty}$ real hypersurface in $\mathbb{C}^{n+1}$, $n\;{\geq}\;1$, locally given as the zero locus of a $C^{\infty}$ real valued function r that is defined on a neighborhood of the reference point $P\;{\in}\;M$. For each k = 1,..., n we present a necessary and sufficient condition for there to exist a complex manifold of dimension k through P that is contained in M, assuming the Levi form has rank n - k at P. The problem is to find an integral manifold of the real 1-form $i{\partial}r$ on M whose tangent bundle is invariant under the complex structure tensor J. We present generalized versions of the Frobenius theorem and make use of them to prove the existence of complex submanifolds.
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