我们研究了实解析的局部等价问题(${\mathcal{<trans\; data-src="C">C类</trans>}}^{\mathit{<trans\; data-src="\omega ">\omega </trans>}}$)超曲面${\mathit{<trans\; data-src="M">M（M）</trans>}}^{\mathrm{<trans\; data-src="5">5</trans>}}<trans\; data-src="\subset ">\subset </trans>{\mathbb{<trans\; data-src="C">C类</trans>}}^{\mathrm{<trans\; data-src="3">三</trans>}}$在一些全纯坐标系中$<trans\; data-src="(">(</trans>{\mathit{<trans\; data-src="z">z（z）</trans>}}_{\mathrm{<trans\; data-src="1">1</trans>}}<trans\; data-src=",">，</trans>{\mathit{<trans\; data-src="z">z（z）</trans>}}_{\mathrm{<trans\; data-src="2">2</trans>}}<trans\; data-src=",">，</trans>\mathit{<trans\; data-src="w">w个</trans>}<trans\; data-src=")">)</trans><trans\; data-src="\in ">\in </trans>{\mathbb{<trans\; data-src="C">C类</trans>}}^{\mathrm{<trans\; data-src="3">三</trans>}}$具有$\mathit{<trans\; data-src="w">w个</trans>}<trans\; data-src="=">=</trans>\mathit{<trans\; data-src="u">u个</trans>}<trans\; data-src="+">+</trans>\sqrt{<trans\; data-src="-">-</trans>\mathrm{<trans\; data-src="1">1</trans>}}\mathit{<trans\; data-src="v">v（v）</trans>}$，是固执的在这种意义上，它们的图形功能

$$\mathit{<trans\; data-src="u">u个</trans>}<trans\; data-src="=">=</trans>\mathit{<trans\; data-src="F">F类</trans>}<trans\; data-src="(">(</trans>{\mathit{<trans\; data-src="z">z（z）</trans>}}_{\mathrm{<trans\; data-src="1">1</trans>}}<trans\; data-src=",">，</trans>{\mathit{<trans\; data-src="z">z（z）</trans>}}_{\mathrm{<trans\; data-src="2">2</trans>}}<trans\; data-src=",">，</trans>{\stackrel{<trans\; data-src="‾">‾</trans>}{\mathit{<trans\; data-src="z">z（z）</trans>}}}_{\mathrm{<trans\; data-src="1">1</trans>}}<trans\; data-src=",">，</trans>{\stackrel{<trans\; data-src="‾">‾</trans>}{\mathit{<trans\; data-src="z">z（z）</trans>}}}_{\mathrm{<trans\; data-src="2">2</trans>}}<trans\; data-src=")">)</trans>$$

独立于v（v）具体来说，我们研究了该群体${\mathsf{<trans\; data-src="Hol">霍尔</trans>}}_{\mathsf{<trans\; data-src="rigid">固执的</trans>}}<trans\; data-src="(">(</trans>\mathit{<trans\; data-src="M">M（M）</trans>}<trans\; data-src=")">)</trans>$属于固执的形式的局部双全纯变换

$$<trans\; data-src="(">(</trans>{\mathit{<trans\; data-src="z">z（z）</trans>}}_{\mathrm{<trans\; data-src="1">1</trans>}}<trans\; data-src=",">，</trans>{\mathit{<trans\; data-src="z">z（z）</trans>}}_{\mathrm{<trans\; data-src="2">2</trans>}}<trans\; data-src=",">，</trans>\mathit{<trans\; data-src="w">w个</trans>}<trans\; data-src=")">)</trans><trans\; data-src="⟼">⟼</trans><trans\; data-src="(">(</trans>{\mathit{<trans\; data-src="f">（f）</trans>}}_{\mathrm{<trans\; data-src="1">1</trans>}}<trans\; data-src="(">(</trans>{\mathit{<trans\; data-src="z">z（z）</trans>}}_{\mathrm{<trans\; data-src="1">1</trans>}}<trans\; data-src=",">，</trans>{\mathit{<trans\; data-src="z">z（z）</trans>}}_{\mathrm{<trans\; data-src="2">2</trans>}}<trans\; data-src=")">)</trans><trans\; data-src=",">，</trans>{\mathit{<trans\; data-src="f">（f）</trans>}}_{\mathrm{<trans\; data-src="2">2</trans>}}<trans\; data-src="(">(</trans>{\mathit{<trans\; data-src="z">z（z）</trans>}}_{\mathrm{<trans\; data-src="1">1</trans>}}<trans\; data-src=",">，</trans>{\mathit{<trans\; data-src="z">z（z）</trans>}}_{\mathrm{<trans\; data-src="2">2</trans>}}<trans\; data-src=")">)</trans><trans\; data-src=",">，</trans>\mathit{<trans\; data-src="a">一</trans>}\mathit{<trans\; data-src="w">w个</trans>}<trans\; data-src="+">+</trans>\mathit{<trans\; data-src="g">克</trans>}<trans\; data-src="(">(</trans>{\mathit{<trans\; data-src="z">z（z）</trans>}}_{\mathrm{<trans\; data-src="1">1</trans>}}<trans\; data-src=",">，</trans>{\mathit{<trans\; data-src="z">z（z）</trans>}}_{\mathrm{<trans\; data-src="2">2</trans>}}<trans\; data-src=")">)</trans><trans\; data-src=")">)</trans><trans\; data-src=",">，</trans>$$

哪里$\mathit{<trans\; data-src="a">一</trans>}<trans\; data-src="\in ">\in </trans>\mathbb{<trans\; data-src="R">R（右）</trans>}<trans\; data-src="\setminus ">\setminus </trans><trans\; data-src="\{">\{</trans>\mathrm{<trans\; data-src="0">0</trans>}<trans\; data-src="\}">\}</trans>$和$\mathit{<trans\; data-src="D">天</trans>}<trans\; data-src="(">(</trans>{\mathit{<trans\; data-src="f">（f）</trans>}}_{\mathrm{<trans\; data-src="1">1</trans>}}<trans\; data-src=",">，</trans>{\mathit{<trans\; data-src="f">（f）</trans>}}_{\mathrm{<trans\; data-src="2">2</trans>}}<trans\; data-src=")">)</trans><trans\; data-src="/">/</trans>\mathit{<trans\; data-src="D">天</trans>}<trans\; data-src="(">(</trans>{\mathit{<trans\; data-src="z">z（z）</trans>}}_{\mathrm{<trans\; data-src="1">1</trans>}}<trans\; data-src=",">，</trans>{\mathit{<trans\; data-src="z">z（z）</trans>}}_{\mathrm{<trans\; data-src="2">2</trans>}}<trans\; data-src=")">)</trans><trans\; data-src="\ne ">\ne </trans>\mathrm{<trans\; data-src="0">0</trans>}$保持超曲面的刚性。

在执行Cartan类型还原到适当的$<trans\; data-src="\{">\{</trans>\mathit{<trans\; data-src="e">e（电子）</trans>}<trans\; data-src="\}">\}</trans>$-结构，我们发现二主不变量${\mathit{<trans\; data-src="I">我</trans>}}_{\mathrm{<trans\; data-src="0">0</trans>}}$和${\mathit{<trans\; data-src="V">V（V）</trans>}}_{\mathrm{<trans\; data-src="0">0</trans>}}$，我们用绘图函数的5个射流明确表示F类属于M（M）.相同的消失$\mathrm{<trans\; data-src="0">0</trans>}<trans\; data-src="\equiv ">\equiv </trans>{\mathit{<trans\; data-src="I">我</trans>}}_{\mathrm{<trans\; data-src="0">0</trans>}}<trans\; data-src="(">(</trans>{\mathit{<trans\; data-src="J">J型</trans>}}^{\mathrm{<trans\; data-src="5">5</trans>}}\mathit{<trans\; data-src="F">F类</trans>}<trans\; data-src=")">)</trans><trans\; data-src="\equiv ">\equiv </trans>{\mathit{<trans\; data-src="V">V（V）</trans>}}_{\mathrm{<trans\; data-src="0">0</trans>}}<trans\; data-src="(">(</trans>{\mathit{<trans\; data-src="J">J型</trans>}}^{\mathrm{<trans\; data-src="5">5</trans>}}\mathit{<trans\; data-src="F">F类</trans>}<trans\; data-src=")">)</trans>$则为M（M）在当地严格双全纯到已知模型超曲面

$${\mathit{<trans\; data-src="M">M（M）</trans>}}_{\mathsf{<trans\; data-src="LC">信用证</trans>}}<trans\; data-src=":">:</trans>\mathit{<trans\; data-src="u">u个</trans>}<trans\; data-src="=">=</trans>\frac{{\mathit{<trans\; data-src="z">z（z）</trans>}}_{\mathrm{<trans\; data-src="1">1</trans>}}{\stackrel{<trans\; data-src="‾">‾</trans>}{\mathit{<trans\; data-src="z">z（z）</trans>}}}_{\mathrm{<trans\; data-src="1">1</trans>}}<trans\; data-src="+">+</trans>\mathrm{<trans\; data-src="1">1</trans>}<trans\; data-src="/">/</trans>\mathrm{<trans\; data-src="2">2</trans>}{\mathit{<trans\; data-src="z">z（z）</trans>}}_{\mathrm{<trans\; data-src="1">1</trans>}}^{\mathrm{<trans\; data-src="2">2</trans>}}{\stackrel{<trans\; data-src="‾">‾</trans>}{\mathit{<trans\; data-src="z">z（z）</trans>}}}_{\mathrm{<trans\; data-src="2">2</trans>}}<trans\; data-src="+">+</trans>\mathrm{<trans\; data-src="1">1</trans>}<trans\; data-src="/">/</trans>\mathrm{<trans\; data-src="2">2</trans>}{\stackrel{<trans\; data-src="‾">‾</trans>}{\mathit{<trans\; data-src="z">z（z）</trans>}}}_{\mathrm{<trans\; data-src="1">1</trans>}}^{\mathrm{<trans\; data-src="2">2</trans>}}{\mathit{<trans\; data-src="z">z（z）</trans>}}_{\mathrm{<trans\; data-src="2">2</trans>}}}{\mathrm{<trans\; data-src="1">1</trans>}<trans\; data-src="-">-</trans>{\mathit{<trans\; data-src="z">z（z）</trans>}}_{\mathrm{<trans\; data-src="2">2</trans>}}{\stackrel{<trans\; data-src="‾">‾</trans>}{\mathit{<trans\; data-src="z">z（z）</trans>}}}_{\mathrm{<trans\; data-src="2">2</trans>}}}<trans\; data-src=".">.</trans>$$

我们始终坚持$\mathsf{<trans\; data-src="dim">昏暗的</trans>}{\mathsf{<trans\; data-src="Hol">霍尔</trans>}}_{\mathsf{<trans\; data-src="rigid">固执的</trans>}}<trans\; data-src="(">(</trans>\mathit{<trans\; data-src="M">M（M）</trans>}<trans\; data-src=")">)</trans><trans\; data-src="\le ">\le </trans>\mathrm{<trans\; data-src="7">7</trans>}<trans\; data-src="=">=</trans>\mathsf{<trans\; data-src="dim">昏暗的</trans>}{\mathsf{<trans\; data-src="Hol">霍尔</trans>}}_{\mathsf{<trans\; data-src="rigid">固执的</trans>}}<trans\; data-src="(">(</trans>{\mathit{<trans\; data-src="M">M（M）</trans>}}_{\mathsf{<trans\; data-src="LC">信用证</trans>}}<trans\; data-src=")">)</trans>$.

如果这两个主要不变量之一${\mathit{<trans\; data-src="I">我</trans>}}_{\mathrm{<trans\; data-src="0">0</trans>}}<trans\; data-src="\not\equiv ">\not\equiv </trans>\mathrm{<trans\; data-src="0">0</trans>}$或${\mathit{<trans\; data-src="V">V（V）</trans>}}_{\mathrm{<trans\; data-src="0">0</trans>}}<trans\; data-src="\not\equiv ">\not\equiv </trans>\mathrm{<trans\; data-src="0">0</trans>}$不会完全消失，那么在两个Zarisk-open集中的任何一个上$<trans\; data-src="\{">\{</trans>\mathit{<trans\; data-src="p">对</trans>}<trans\; data-src="\in ">\in </trans>\mathit{<trans\; data-src="M">M（M）</trans>}<trans\; data-src=":">:</trans>{\mathit{<trans\; data-src="I">我</trans>}}_{\mathrm{<trans\; data-src="0">0</trans>}}<trans\; data-src="(">(</trans>\mathit{<trans\; data-src="p">对</trans>}<trans\; data-src=")">)</trans><trans\; data-src="\ne ">\ne </trans>\mathrm{<trans\; data-src="0">0</trans>}<trans\; data-src="\}">\}</trans>$或$<trans\; data-src="\{">\{</trans>\mathit{<trans\; data-src="p">对</trans>}<trans\; data-src="\in ">\in </trans>\mathit{<trans\; data-src="M">M（M）</trans>}<trans\; data-src=":">:</trans>{\mathit{<trans\; data-src="V">V（V）</trans>}}_{\mathrm{<trans\; data-src="0">0</trans>}}<trans\; data-src="(">(</trans>\mathit{<trans\; data-src="p">对</trans>}<trans\; data-src=")">)</trans><trans\; data-src="\ne ">\ne </trans>\mathrm{<trans\; data-src="0">0</trans>}<trans\; data-src="\}">\}</trans>$，我们证明了刚性超曲面之间的刚性等价问题可简化为某个五维曲面的等价问题$<trans\; data-src="\{">\{</trans>\mathit{<trans\; data-src="e">e（电子）</trans>}<trans\; data-src="\}">\}</trans>$-上的结构M（M）也就是说，我们在${\mathit{<trans\; data-src="M">M（M）</trans>}}^{\mathrm{<trans\; data-src="5">5</trans>}}$.因此$\mathsf{<trans\; data-src="dim">昏暗的</trans>}{\mathsf{<trans\; data-src="Hol">霍尔</trans>}}_{\mathsf{<trans\; data-src="rigid">固执的</trans>}}<trans\; data-src="(">(</trans>\mathit{<trans\; data-src="M">M（M）</trans>}<trans\; data-src=")">)</trans>$从7降到5，说明间隙现象。