Explicit construction of Lagrangian isometric immersion of a real-space-form Mn(c) into a complex-space-form M˜n(4c)
Explicit construction of Lagrangian isometric immersion of a real-space-form Mn(c) into a complex-space-form M˜n(4c)
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DOI：
10.1017/s0305004101005783
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发表时间：
2002-05
影响因子：
0.8
通讯作者：
Y. Oh
中科院分区：
文献类型：
--
作者：
Y. Oh
在[4]中，证明了当扭量形式是扭闭的时，存在一个由常截面曲率c的实空间形式Mn（c）到常截面曲率4c的复空间形式Mn（4c）的“唯一的”适应拉格朗日等距浸入.相反，如果L：Mn（c）→ M n（4c）是实空间形式Mn（c）到复空间形式M n（4c）的非全测地拉格朗日等距浸入，则Mn（c）允许一个适当的扭积分解，其扭积分解具有扭闭扭量形式，浸入L由相应的扭积分解的适当拉格朗日等距浸入确定.很自然地，对于c = 0，c > 0和c < 0的每种情况，要求实空间形式Mn（c）到复空间形式M n（4c）的扭曲乘积分解的适应拉格朗日等距浸入的显式表达式。
In [4], it is proved that there exists a ‘unique’ adapted Lagrangian isometric immersion of a real-space-form Mn(c) of constant sectional curvature c into a complex-space-form M˜n(4c) of constant sectional curvature 4c associated with each twisted product decomposition of a real-space-form if its twistor form is twisted closed. Conversely, if L: Mn(c) → M˜n(4c) is a non-totally geodesic Lagrangian isometric immersion of a real-space-form Mn(c) into a complex-space-form M˜n(4c), then Mn(c) admits an appropriate twisted product decomposition with twisted closed twistor form and, moreover, the immersion L is determined by the corresponding adapted Lagrangian isometric immersion of the twisted product decomposition. It is natural to ask the explicit expressions of adapted Lagrangian isometric immersions of twisted product decompositions of real-space-forms Mn(c) into complex-space-forms M˜n(4c) for each case: c = 0, c > 0 and c < 0.