A characterization of the Veronese varieties
A characterization of the Veronese varieties
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维罗纳品种的特征
DOI：
10.1017/s0027763000017220
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发表时间：
1976
影响因子：
0.8
通讯作者：
K. Nomizu
中科院分区：
文献类型：
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作者：
K. Nomizu
设Pm（C）是m维复射影空间。在前一篇文章[2]中，我们证明了定理A.设f是n维连通完备Kaehler流形Mn在Pm（C）中的Kaehler浸入.若Mn中每一测地线τ的像f（τ）位于Pm（C）的复射影直线P1（C）上，则f（Mn）是Pm（C）的复射影子空间，且f是全测地线.
Let Pm(C) be the complex projective space of dimension m. In a previous paper [2] we have proved THEOREM A. Let f be a Kaehlerian immersion of a connected, complete Kaehler manifold Mn of dimension n into Pm(C). If the image f(τ) of each geodesic τ in Mn lies in a complex projective line P1(C) of Pm(C), then f(Mn) is a complex projective subspace of Pm(C), and f is totally geodesic.