**Аннотация:**
We will cover applications of the relationship between
homogeneous 2-nondegenerate CR manifolds of hypersurface type and their
modified CR symbols, a local invariant of their structure recently
defined (in joint work with Igor Zelenko) that also encodes the basic
local invariants sometimes referred to as their generalized Levi forms.
From this relationship we will derive algebraic criteria for a set of
generalized Levi forms to admit a homogeneous model, and, in particular,
obtain obstructions to homogeneity expressed in terms of the local
invariants at a point. From these criteria, we obtain the classification
up to local equivalence of 2-nondegenerate real hypersurfaces in complex
4-space that are locally equivalent to homogeneous CR manifolds whose
symmetry groups have maximal dimension relative to their modified CR
symbols. In total, there are 9 CR structures in this classification. In
higher dimensions, by applying a Tanaka-theoretic algebraic prolongation
to special reductions of the modified symbols we obtain estimates on the
homogeneous models' symmetry group dimensions.
**Язык доклада:** английский
**Website:**
https://mi-ras-ru.zoom.us/j/6119310351?pwd=anpleGlnYVFXNEJnemRYZk5kMWNiQT09
^{*} *ID: 611 931 0351. Password: 5MAVBP.* |