Equivalences of PDE systems associated to degenerate para-CR structures: foundational aspects
نویسندگان
چکیده
Let $${\mathbb {K}}= {\mathbb {R}}$$ or {C}}$$ . We study basic invariants of submanifolds solutions $${\mathscr {M}} = \{ y Q(x,a,b)\} \{b P(a,x,y)\}$$ in coordinates $$x \in {K}}^{n\geqslant 1}$$ , $$y {K}}$$ $$a {K}}^{m\geqslant $$b under split-diffeomorphisms $$(x,y,a,b) \,\longmapsto \, \big ( f(x,y),\,g(x,y),\,\varphi (a,b),\,\psi (a,b) )$$ Two Levi forms exist, and have the same rank $$r \leqslant \mathsf{min}(n,m)$$ If {M}}$$ is k-nondegenerate with respect to parameters l-nondegenerate variables, $$\mathsf{Aut}({\mathscr {M}})$$ a local Lie group dimension: $$\begin{aligned} \mathsf{dim}\, \mathsf{Aut}({\mathscr {M}}) (n+1)\, \genfrac(){0.0pt}1{n+1+2k+2l}{n+1} + (m+1)\, \genfrac(){0.0pt}1{m+1+2k+2l}{m+1}. \end{aligned}$$ Mainly, our goal set up foundational material addressed CR geometers. focus on $$n m 2$$ assuming 1$$ In (x, y, z, a, b, c), equation is: z c xa \beta \,xxb {\underline{\beta }}\,yaa c\,\mathrm{O}_{x,y,a,b}(2) \mathrm{O}_{x,y,a,b,c}(4), $$\beta $$ $${\underline{\beta }}$$ representing two 2-nondegeneracy at 0. The associated para-CR pde system: z_y F\big (x,y,z,z_x,z_{xx}\big ) \quad z_{xxx} H\big ), satisfies $$F_{z_{xx}} \equiv 0$$ from degeneracy. show details that hypothesis variables equivalent $$F_{z_x z_x} \ne This gives CR-geometric meaning first relative differential encountered independently another paper, joint Paweł Nurowski.
منابع مشابه
Foundational aspects of nonlocality
Nonlocality refers to correlations between spatially separated parties that are stronger than those explained by the existence of local hidden variables. Quantum mechanics is known to allow some nonlocal correlations between particles in a phenomena known as entanglement. We explore several aspects of nonlocality in general and how they relate to quantum mechanics. First, we construct a hierarc...
متن کاملReduction of Five-Dimensional Uniformly Levi Degenerate CR Structures to Absolute Parallelisms
An almost CR-structure on a smooth manifoldM is a subbundle H(M) ⊂ T (M) of the tangent bundle of even rank endowed with operators of complex structure Jp : Hp(M) → Hp(M), J p = −id, that smoothly depend on p. A manifold equipped with an almost CR-structure is called an almost CR-manifold. The subspaces Hp(M) are called the complex tangent spaces to M , and their complex dimension, denoted by C...
متن کاملFoundational aspects of multiscale digitization
In this article, we describe the theoretical foundations of the Ω-arithmetization. This method provides a multi-scale discretization of a continuous function that is a solution of a differential equation. This discretization process is based on the Harthong-Reeb line HRω. The HarthongReeb line is a linear space that is both discrete and continuous. This strange line HRω stems from a nonstandard...
متن کاملFoundational Aspects of Multiscale Digitisation
In this article, we describe the theoretical foundations of the Ω-arithmetization. This method provides a multi-scale discretization of a continuous function that is a solution of a differential equation. This discretization process is based on the Harthong-Reeb line HRω. The HarthongReeb line is a linear space that is both discrete and continuous. This strange line HRω stems from a nonstandard...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Partial Differential Equations And Applications
سال: 2021
ISSN: ['2662-2971', '2662-2963']
DOI: https://doi.org/10.1007/s42985-021-00138-z