On Degenerate Para-CR Structures: Cartan Reduction and Homogeneous Models
نویسندگان
چکیده
Motivated by recent works in Levi degenerate CR geometry, this article endeavors to study the wider and more flexible para-CR structures for which constraint of invariancy under complex conjugation is relaxed. We consider 5-dimensional whose forms are constant rank 1 that 2-nondegenerate both with respect parameters variables. Eliminating parameters, such may be represented modulo point transformations pairs PDEs zy = F(x,y,z,zx) & zxxx H(x,y,z,zx,zxx), F independent zxx $F_{z_{x}z_{x}} \neq 0$ , completely integrable ${D_{x}^{3}} {\Delta }_{y} H$ Performing at an advanced level Cartan’s method equivalence, we determine all concerned homogeneous models, together their symmetries:
منابع مشابه
Maximally Homogeneous Para-cr Manifolds of Semisimple Type
An almost para-CR structure on a manifold M is given by a distribution HM ⊂ TM together with a field K ∈ Γ(End(HM)) of involutive endomorphisms of HM . If K satisfies an integrability condition, then (HM,K) is called a para-CR structure. The notion of maximally homogeneous para-CR structure of a semisimple type is given. A classification of such maximally homogeneous para-CR structures is given...
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 کامل1 F eb 2 00 6 Homogeneous Levi degenerate CR - manifolds in dimension 5
Levi nondegenerate real-analytic hypersurfaces M ⊂ are well understood due to the seminal results of Tanaka [17] and Chern-Moser[5], where a complete set of local invariants for M has been defined. At the other extreme are those hypersurfaces which are locally CR-equivalent to a product M ×, (take the real hyperplanes in as a simple example). In-between there is a huge and much less underst...
متن کاملPara-CR structures of codimension 2 on tangent bundles in Riemann-Finsler geometry
We determine a 2-codimensional para-CR structure on the slit tangent bundle T0M of a Finsler manifold (M,F ) by imposing a condition regarding the almost paracomplex structure P associated to F when restricted to the structural distribution of a framed para-f -structure. This condition is satisfied when (M,F ) is of scalar flag curvature (particularly constant) or if the Riemannian manifold (M,...
متن کاملHomogeneous Para - Kähler Einstein
A para-Kähler manifold can be defined as a pseudoRiemannian manifold (M, g) with a parallel skew-symmetric paracomplex structures K, i.e. a parallel field of skew-symmetric endomorphisms with K = Id or, equivalently, as a symplectic manifold (M, ω) with a bi-Lagrangian structure L, i.e. two complementary integrable Lagrangian distributions. A homogeneous manifold M = G/H of a semisimple Lie gro...
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: Transformation Groups
سال: 2022
ISSN: ['1531-586X', '1083-4362']
DOI: https://doi.org/10.1007/s00031-022-09746-4