English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

We construct complete normal forms for $5$-dimensional real hypersurfaces in$\mathbb C^3$ which are $2$-nondegenerate and also of Levi non-uniform rankzero at the origin point ${\bf p} =0$. The latter condition means that the rankof the Levi form vanishes at ${\bf p}$ but not identically in a neighborhood ofit. The mentioned hypersurfaces are the only finitely nondegenerate realhypersurfaces in $\mathbb C^3$ for which their complete normal forms wereabsent in the literature. As a byproduct, we also treat the underlyingbiholomorphic equivalence problem between the hypersurfaces. Our primaryapproach in constructing the desired complete normal forms is to utilize thetechniques derived in the theory of equivariant moving frames. It notablyoffers the advantage of systematic and symbolic manipulation of the associatedcomputations.

Complete normal forms for real hypersurfaces in $\mathbb C^3$ at 2-nondegenerate points of Levi non-uniform rank zero