Related papers: Normal forms of para-CR hypersurfaces

We construct a formal normal form for a real 2-codimensional submanifold $M\subset\mathbb{C}^{N+1}$ near a CR singularity approximating the sphere. This result gives a higher dimensional extension of Huang-Yin's normal form in…

It is constructed a formal normal form, using an iterative normalization procedure, for a large class of Real-Smooth Hypersurfaces in Complex Spaces.

We study hypersurfaces either in the De Sitter space $\S_1^{n+1}\subset\R_1^{n+2}$ or in the anti De Sitter space $\H_1^{n+1}\subset\R_2^{n+2}$ whose position vector $\psi$ satisfies the condition $L_k\psi=A\psi+b$, where $L_k$ is the…

We study a class of nondivergence form second-order degenerate linear parabolic equations in $(-\infty, T) \times {\mathbb R}^d_+$ with the homogeneous Dirichlet boundary condition on $(-\infty, T) \times \partial {\mathbb R}^d_+$, where…

This paper present homogeneous CR hypersurfaces satisfying the $CR$-invariant property of being $k$-nondegenerate for an arbitrary integer $k\geq 1$. The construction of such homogeneous manifolds are based on $CR$ algebras defined by…

We compare various definitions of nondegeneracy of the Levi map for real submanifolds of higher codimension in $C^N$ and discuss the generalization to higher codimension of the 2-jet determination for biholomorphisms in the hypersurface…

In the theory of finite type submanifolds, null 2-type submanifolds are the most simple ones, besides 1-type submanifolds (cf. e.g., [3, 12]). In particular, the classification problems of null 2-type hypersurfaces are quite interesting and…

In this paper, we give a complete conformal classification of the regular space-like hypersurfaces in the de Sitter Space $\mathbb{S}^{m+1}_{1}$ with parallel para-Blaschke tensors.

Let $M^3 \subset \mathbb{C}^2$ be a $\mathcal{C}^\omega$ Levi nondegenerate hypersurface. In the literature, Cartan-Moser chains are detected from rather advanced considerations: either from the construction of a Cartan connection…

In this paper, we show how to construct a special class of ruled hypersurfaces in the nonflat complex space forms $\mathbb{CP}^n$ and $\mathbb{C}H^n$. This is done by taking an arbitrary smooth curve in a totally geodesic (complex)…

Searching normal forms for real analytic submanifolds of C^n involves convergence problems. In 1983, J.K. Moser and S.M. Webster provided examples of real analytic surfaces in C^2 having an isolated hyperbolic (in the sense of E. Bishop)…

We prove finite jet determination for (finitely) smooth CR diffeomorphisms of (finitely) smooth Levi degenerate hypersurfaces in $\mathbb{C}^{n+1}$ by constructing generalized stationary discs glued to such hypersurfaces.

The authors study the geometry of lightlike hypersurfaces on pseudo-Riemannian manifolds $(M, g)$ of Lorentzian signature. Such hypersurfaces are of interest in general relativity since they can be models of different types of physical…

Let M be a connected real-analytic hypersurface in N-dimensional complex euclidean space whose Levi form is nondegenerate at some point. We prove that for every point p in M, there exists an integer k=k(M,p) such that germs at p of local…

It was recently shown that under mild assumptions second-order conformally superintegrable systems can be encoded in a $(0,3)$-tensor, called structure tensor. For abundant systems, this approach led to algebraic integrability conditions…

Let M be a CR manifold of hypersurface type, which is Levi degenerate but also satisfying a k-nondegeneracy condition at all points. This might be only if dim M is greater than or equal to 5 and if dim M = 5, then k= 2 at all points. We…

In this article, we consider surfaces in the 3-dimensional Euclidean space E3 without parabolic points which are of finite II-type, that is, they are of finite type, in the sense of B.-Y. Chen, corresponding to the second fundamental form.…

We study a class of second-order degenerate linear parabolic equations in divergence form in $(-\infty, T) \times \mathbb R^d_+$ with homogeneous Dirichlet boundary condition on $(-\infty, T) \times \partial \mathbb R^d_+$, where $\mathbb…

We give a geometric characterization of certain hypersurfaces of cohomogeneity one in the complex projective and hyperbolic planes. We also obtain some partial classifications of austere hypersurfaces and of Levi-flat hypersurfaces with…

We study singular real-analytic Levi-flat hypersurfaces in complex projective space. We define the rank of an algebraic Levi-flat hypersurface and study the connections between rank, degree, and the type and size of the singularity. In…