@article{article_943426, title={Differentiall $ {e} $-structures for equivalences of $ 2 $-nondegenerate Levi rank $ 1 $ hypersurfaces $ M_5 ⊂ \mathbb{C} $}, journal={Constructive Mathematical Analysis}, volume={4}, pages={318–377}, year={2021}, DOI={10.33205/cma.943426}, author={Merker, Jöel and Foo, Wei}, keywords={Levi degenerate CR manifolds, 2-nondegeneracy, G-structures, Cartan method of equivalence, Cartan Lemma, Pocchiola invariants}, abstract={The class <span class="MathJax_Preview" style="color:inherit;"> </span> <span class="mjx-chtml MathJax_CHTML" style="font-size:123%;"> <span class="mjx-math"> <span class="mjx-mrow"> <span class="mjx-msubsup"> <span class="mjx-base"> <span class="mjx-mtext"> <span class="mjx-char MJXc-TeX-main-R" style="padding-top:.441em;padding-bottom:.566em;">IV </span> </span> </span> <span class="mjx-sub" style="font-size:70.7%;vertical-align:-.439em;padding-right:.071em;"> <span class="mjx-mn"> <span class="mjx-char MJXc-TeX-main-R" style="padding-top:.378em;padding-bottom:.316em;">2 </span> </span> </span> </span> </span> </span> <span class="MJX_Assistive_MathML">\sf IV2 </span> </span> of <span class="MathJax_Preview" style="color:inherit;"> </span> <span class="mjx-chtml MathJax_CHTML" style="font-size:123%;"> <span class="mjx-math"> <span class="mjx-mrow"> <span class="mjx-mn"> <span class="mjx-char MJXc-TeX-main-R" style="padding-top:.378em;padding-bottom:.316em;">2 </span> </span> </span> </span> <span class="MJX_Assistive_MathML">2 </span> </span>-nondegenerate constant Levi rank <span class="MathJax_Preview" style="color:inherit;"> </span> <span class="mjx-chtml MathJax_CHTML" style="font-size:123%;"> <span class="mjx-math"> <span class="mjx-mrow"> <span class="mjx-mn"> <span class="mjx-char MJXc-TeX-main-R" style="padding-top:.378em;padding-bottom:.316em;">1 </span> </span> </span> </span> <span class="MJX_Assistive_MathML">1 </span> </span> hypersurfaces <span class="MathJax_Preview" style="color:inherit;"> </span> <span class="mjx-chtml MathJax_CHTML" style="font-size:123%;"> <span class="mjx-math"> <span class="mjx-mrow"> <span class="mjx-msubsup"> <span class="mjx-base" style="margin-right:-.081em;"> <span class="mjx-mi"> <span class="mjx-char MJXc-TeX-math-I" style="padding-top:.441em;padding-bottom:.253em;padding-right:.081em;">M </span> </span> </span> <span class="mjx-sup" style="font-size:70.7%;vertical-align:.513em;padding-left:.22em;padding-right:.071em;"> <span class="mjx-mn"> <span class="mjx-char MJXc-TeX-main-R" style="padding-top:.378em;padding-bottom:.378em;">5 </span> </span> </span> </span> <span class="mjx-mo MJXc-space3"> <span class="mjx-char MJXc-TeX-main-R" style="padding-top:.253em;padding-bottom:.378em;">⊂ </span> </span> <span class="mjx-msubsup MJXc-space3"> <span class="mjx-base"> <span class="mjx-texatom"> <span class="mjx-mrow"> <span class="mjx-mi"> <span class="mjx-char MJXc-TeX-ams-R" style="padding-top:.441em;padding-bottom:.316em;">C </span> </span> </span> </span> </span> <span class="mjx-sup" style="font-size:70.7%;vertical-align:.642em;padding-left:0px;padding-right:.071em;"> <span class="mjx-mn"> <span class="mjx-char MJXc-TeX-main-R" style="padding-top:.378em;padding-bottom:.378em;">3 </span> </span> </span> </span> </span> </span> <span class="MJX_Assistive_MathML">M5⊂C3 </span> </span> is governed by Pocchiola’s two primary invariants <span class="MathJax_Preview" style="color:inherit;"> </span> <span class="mjx-chtml MathJax_CHTML" style="font-size:123%;"> <span class="mjx-math"> <span class="mjx-mrow"> <span class="mjx-msubsup"> <span class="mjx-base" style="margin-right:-.104em;"> <span class="mjx-mi"> <span class="mjx-char MJXc-TeX-math-I" style="padding-top:.441em;padding-bottom:.316em;padding-right:.104em;">W </span> </span> </span> <span class="mjx-sub" style="font-size:70.7%;vertical-align:-.212em;padding-right:.071em;"> <span class="mjx-mn"> <span class="mjx-char MJXc-TeX-main-R" style="padding-top:.378em;padding-bottom:.378em;">0 </span> </span> </span> </span> </span> </span> <span class="MJX_Assistive_MathML">W0 </span> </span> and <span class="MathJax_Preview" style="color:inherit;"> </span> <span class="mjx-chtml MathJax_CHTML" style="font-size:123%;"> <span class="mjx-math"> <span class="mjx-mrow"> <span class="mjx-msubsup"> <span class="mjx-base" style="margin-right:-.078em;"> <span class="mjx-mi"> <span class="mjx-char MJXc-TeX-math-I" style="padding-top:.441em;padding-bottom:.316em;padding-right:.078em;">J </span> </span> </span> <span class="mjx-sub" style="font-size:70.7%;vertical-align:-.212em;padding-right:.071em;"> <span class="mjx-mn"> <span class="mjx-char MJXc-TeX-main-R" style="padding-top:.378em;padding-bottom:.378em;">0 </span> </span> </span> </span> </span> </span> <span class="MJX_Assistive_MathML">J0 </span> </span>. Their vanishing characterizes equivalence of such a hypersurface <span class="MathJax_Preview" style="color:inherit;"> </span> <span class="mjx-chtml MathJax_CHTML" style="font-size:123%;"> <span class="mjx-math"> <span class="mjx-mrow"> <span class="mjx-msubsup"> <span class="mjx-base" style="margin-right:-.081em;"> <span class="mjx-mi"> <span class="mjx-char MJXc-TeX-math-I" style="padding-top:.441em;padding-bottom:.253em;padding-right:.081em;">M </span> </span> </span> <span class="mjx-sup" style="font-size:70.7%;vertical-align:.513em;padding-left:.22em;padding-right:.071em;"> <span class="mjx-mn"> <span class="mjx-char MJXc-TeX-main-R" style="padding-top:.378em;padding-bottom:.378em;">5 </span> </span> </span> </span> </span> </span> <span class="MJX_Assistive_MathML">M5}, number={3}, publisher={Tuncer ACAR}