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In this paper, we study the existence of a complete holomorphic vector field on a strongly pseudoconvex complex manifold admitting a negatively curved complete Kähler–Einstein metric and a discrete sequence of automorphisms. Using the method of potential scaling, we will show that there is a potential function of the Kähler–Einstein metric whose differential has a constant length. Then, we will construct a complete holomorphic vector field from the gradient vector field of the potential function.
相似文献2.
We will prove that the automorphism groups of the strongly pseudoconvex model domains in almost complex manifolds are isomorphically embedded into the automorphism group of the unit ball. 相似文献
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We study the almost complex manifold and its symmetry algebra, the set of germs of infinitesimal automorphisms. The main result
is that there is a certain condition to a torsion bundle under which the dimension of the symmetry algebra can not exceed
4 in the case of complex dimension 2. We will give an example which attains the maximal dimension 4, and another example without
non-degeneracy whose symmetry algebra is of infinite dimension. 相似文献
4.
Let (M,J) be a germ of an almost complex manifold of real dimension 2m and let n (n<m) be an integer. We study a necessary and sufficient condition for M to admit an integrable submanifold N of complex dimension n. If n=m−1, we find defining functions of N explicitly from the coefficients of the torsion tensor. For J obtained by small perturbation of the standard complex structure of ℂ
m
this condition is given as an overdetermined system of second order PDEs on the perturbation. The proof is based on the rank
conditions of the Nijenhuis tensor and application of the Newlander-Nirenberg theorem. We give examples of almost complex
structures on ℂ3: the ones with a single complex submanifold of dimension 2 and the ones with 1-parameter or 2-parameter families of complex
submanifolds of dimension 2. 相似文献
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Kang-Hyurk Lee 《Transactions of the American Mathematical Society》2006,358(5):2057-2069
We present a generalization of Cartan's uniqueness theorem to the almost complex manifolds.
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