Related papers: Real-Smooth Hypersurfaces in $\mathbb{C}^{N+1}$
It is constructed a normal form for a class of real-smooth surfaces M\subset\mathbb{C}^{2} defined near a degenerate CR singularity.
It is formally constructed a normal form for a class of real-formal surfaces defined near a CR Singularity.
For any positive integer $r$, we construct a smooth complex projective rational surface which has at least $r$ real forms not isomorphic over $\mathbb{R}$.
It is constructed a Formal Normal Form for a Special Class of Real-Smooth Submanfolds in $\mathbb{C}^{2N}$.
We provide normal forms for singularities of analytic hypersurfaces in $({\mathbb C}^n,0)$, using holomorphic vector fields.
We describe a procedure for constructing formal normal forms of holomorphic maps with a hypersurface of fixed points, and we apply it to obtain a complete list of formal normal forms for 2-dimensional holomorphic maps tangential to a curve…
We construct examples of inhomogeneous isoparametric real hypersurfaces in complex hyperbolic spaces.
We classify all real hypersurfaces with constant principal curvatures in the complex hyperbolic plane.
We construct normal forms for Levi degenerate hypersurfaces of finite type in $\mathbb C^2$. As one consequence, an explicit solution to the problem of local biholomorphic equivalence is obtained. Another consequence determines the…
We classify all real hypersurfaces with three distinct constant principal curvatures in complex hyperbolic spaces of dimension greater than two.
In this paper we introduce the fourth fundamental form for the hypersurfaces in $H^{n+1}$ and the space-like hypersurfaces in $S_{1}^{n+1}$ and discuss the conformality of the normal Gauss maps of the hypersurfaces in $H^{n+1}$ and…
We study translation minimal hypersurfaces and separable minimal hypersurfaces in the ($n+1$)-space with $2m$-norm.
We study the geometry of homogeneous hypersurfaces and their focal sets in complex hyperbolic spaces. In particular, we provide a characterization of the focal set in terms of its second fundamental form and determine the principal…
In this article we provide a general construction when $n\ge3$ for immersed in Euclidean $(n+1)$-space, complete, smooth, constant mean curvature hypersurfaces of finite topological type (in short CMC $n$-hypersurfaces). More precisely our…
The techniques developed by Butscher in arXiv:math/0703469 for constructing constant mean curvature (CMC) hypersurfaces in the (n+1)-sphere by gluing together spherical building blocks are generalized to handle less symmetric initial…
We construct families of hyperbolic hypersurfaces $X_d\subset\mathbb{P}^{n+1}(\mathbb{C})$ of degree $d\geq {\textstyle{(\frac{n+3}{2})^2}}$.
We classify isoparametric hypersurfaces in complex hyperbolic spaces.
It is proved that the geometry of lightlike hypersurfaces of the de Sitter space S^{n+1}_1 is directly connected with the geometry of hypersurfaces of the conformal space C^n. This connection is applied for a construction of an invariant…
We construct the first examples of rationally convex surfaces in the complex plane with hyperbolic complex tangencies. In fact, we give two very different types of rationally convex surfaces: those that admit analytic fillings by…
We consider hypersurfaces of products $M\times\mathbb R$ with constant $r$-th mean curvature $H_r\ge 0$ (to be called $H_r$-hypersurfaces), where $M$ is an arbitrary Riemannian $n$-manifold. We develop a general method for constructing…