On the holomorphically projective correspondence between Kählerian spaces preserving complex structure
On the holomorphically projective correspondence between Kählerian spaces preserving complex structure
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关于保留复杂结构的凯勒空间之间的全纯射影对应
DOI：
10.14492/hokmj/1381758799
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发表时间：
1974
影响因子：
0.5
通讯作者：
Toshio Sakaguchi
中科院分区：
文献类型：
--
作者：
Toshio Sakaguchi
设（M^{n}，g）和（M^{\prime n}，g ∈ '（n>2）分别是具有正定度量张量g和g'的n维黎曼空间.经典微分几何中著名的贝尔特拉米定理（Beltrami's theorem）（见[1]^{1]} \S 40）指出，如果（M^{n}，g）是常曲率的，那么与它射影对应的空间必然是常曲率的。N. S. Sinyukov [5]将上述定理推广到了（M^{n}，g）与（M^{\prime n}，g）'的局部对称的非仿射射影对应。进一步W。Roter [4]和J.罗宾逊和J. D. Zund [3]推广了N. S. Sinyukov定理的情况下，当（M^{\prime n}，g）'是经常性的。另一方面，T. tsuki和Y. Tashiro [2]研究了K\“ahler空间之间的全纯投射对应。令（M^{n}，
Let (M^{n}, g) and (M^{\prime n}, g)’(n>2) be n-dimensional Riemannian spaces with positive definite metric tensors g and g’, respectively. The celebrated Beltrami’s theorem (see [1]^{1)} \S 40) of classical differential geometry states that if (M^{n}, g) is of constant curvature then the space which is in projective correspondence with it is necessarily of constant curvature. N. S. Sinyukov [5] has generalized the above theorem to the non-affine projective correspondence of (M^{n}, g) with (M^{\prime n}, g)’ which is locally symmetric. Further W. Roter [4] and J. Robinson and J. D. Zund [3] have generalized N. S. Sinyukov’s theorem to the case when (M^{\prime n}, g)’ is recurrent. On the other hand T. tsuki and Y. Tashiro [2] have studied hol0morphically projective correspondences between K\"ahlerian spaces. Let (M^{n},