An umbilical point on a non-real-analytic surface
An umbilical point on a non-real-analytic surface
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非实解析曲面上的脐点
DOI：
10.32917/hmj/1150997863
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发表时间：
2003
影响因子：
0.2
通讯作者：
N. Ando
中科院分区：
文献类型：
--
作者：
N. Ando
设F是一个二元光滑函数，在φ 0; 0 φ处为零，在φ 0; 0 φ的穿孔邻域上为正。则函数expr 1=F 1光滑地延拓到R 0; 0 0，且R3的原点o是其图的脐点.在本文中，我们将研究的主要分布的行为在o周围的条件下，log F的梯度向量场的范数是有界的从下到一个正的常数上的穿孔邻域的000; 000。
Let F be a smooth function of two variables which is zero at ð0; 0Þ and positive on a punctured neighborhood of ð0; 0Þ. Then the function expð� 1=F Þ is smoothly extended to ð0; 0Þ and then the origin o of R 3 is an umbilical point of its graph. In this paper, we shall study the behavior of the principal distributions around o on condition that the norm of the gradient vector field of log F is bounded from below by a positive constant on a punctured neighborhood of ð0; 0Þ.