English
norskBlar i forfatter "Doubrov, Boris"
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Classification of Simply-Transitive Levi Non-Degenerate Hypersurfaces in C^3
(Journal article; Tidsskriftartikkel; Peer reviewed, 2021-06-24)Holomorphically homogeneous Cauchy–Riemann (CR) real hypersurfaces M<sup>3</sup>⊂C<sup>2</sup> were classified by Élie Cartan in 1932. In the next dimension, we complete the classification of simply-transitive Levi non-degenerate hypersurfaces M<sup>5</sup>⊂C<sup>3</sup> using a novel Lie algebraic approach independent of any earlier classifications of abstract Lie algebras. Central to our approach ... -
Classification of simply-transitive Levi non-degenerate hypersurfaces in C^3
(Journal article; Tidsskriftartikkel; Peer reviewed, 2021-06-24)Holomorphically homogeneous Cauchy–Riemann (CR) real hypersurfaces <i>M<i/><sup>3</sup>⊂C<sup>2</sup> were classified by Élie Cartan in 1932. In the next dimension, we complete the classification of simply-transitive Levi non-degenerate hypersurfaces <i>M<i/><sup>5</sup>⊂C<sup>3</sup> using a novel Lie algebraic approach independent of any earlier classifications of abstract Lie algebras. Central ... -
Homogeneous integrable Legendrian contact structures in dimension five
(Journal article; Tidsskriftartikkel; Peer reviewed, 2019-07-04)We consider Legendrian contact structures on odd-dimensional complex analytic manifolds. We are particularly interested in integrable structures, which can be encoded by compatible complete systems of second order PDEs on a scalar function of many independent variables and considered up to point transformations. Using the techniques of parabolic differential geometry, we compute the associated ... -
Homogeneous Levi non-degenerate hypersurfaces in C3
(Journal article; Tidsskriftartikkel; Peer reviewed, 2020-06-09)We classify all (locally) homogeneous Levi non-degenerate real hypersurfaces in C<sup>3</sup> with symmetry algebra of dimension ≥6. -
Homogeneous Levi non-degenerate hypersurfaces in C^3
(Journal article; Tidsskriftartikkel; Peer reviewed, 2020-06-09)We classify all (locally) homogeneous Levi non-degenerate real hypersurfaces in C<sup>3</sup> with symmetry algebra of dimension ≥6. -
Integrable Systems in Four Dimensions Associated with Six-Folds in Gr(4, 6)
(Journal article; Tidsskriftartikkel, 2018-01-29)Let Gr(d, n) be the Grassmannian of <i>d</i>-dimensional linear subspaces of an <i>n</i>-dimensional vector space <i>V</i>. A submanifold <i>X</i> ⊂ Gr(<i>d, n</i>) gives rise to a differential system Σ(X) that governs <i>d</i>-dimensional submanifolds of <i>V</i> whose Gaussian image is contained in <i>X</i>. We investigate a special case of this construction where <i>X</i> is a six-fold in Gr(4, ... -
On a class of integrable systems of Monge-Ampère type
(Journal article; Tidsskriftartikkel; Peer reviewed, 2017-06-08)We investigate a class of multi-dimensional two-component systems of Monge-Ampère type that can be viewed as generalisations of heavenly type equations appearing in a self-dual Ricci-flat geometry. Based on the Jordan-Kronecker theory of the skew-symmetric matrix pencils, a classification of normal forms of such systems is obtained. All two-component systems of Monge-Ampère type turn out to be ... -
On C-class equations
(Journal article; Tidsskriftartikkel; Peer reviewed, 2023-09-29)The concept of a C-class of differential equations goes back to E. Cartan with the upshot that generic equations in a C-class can be solved without integration. While Cartan’s definition was in terms of differential invariants being first integrals, all results exhibiting C-classes that we are aware of are based on the fact that a canonical Cartan geometry associated to the equations in the class ...
