Related papers: Hopf Real Hypersurfaces in the Indefinite Complex …

Using deformations of foliations to contact structures as well as rigidity properties of Anosov foliations we provide infinite families of examples which show that the space of taut foliations in a given homotopy class of plane fields is in…

A Hopf hypersurface in complex hyperbolic space CH^n is one in which the complex structure applied to the normal vector is a principal direction at each point. In this paper, Hopf hypersurfaces for which the corresponding principal…

We prove that proper pseudo-holomorphic maps between strictly pseudoconvex regions in almost complex manifolds extend to the boundary. The key point is that the Jacobian is far from zero near the boundary, and the proof is mainly based on…

We study curvature restrictions of Levi-flat real hypersurfaces in complex projective planes, whose existence is in question. We focus on its totally real Ricci curvature, the Ricci curvature of the real hypersurface in the direction of the…

We study the classification of smooth toroidal compactifications of nonuniform ball quotients in the sense of Kodaira and Enriques. Moreover, several results concerning the Riemannian and complex algebraic geometry of these spaces are…

Using the methods of moving frames and exterior differential systems, we show that there exist Hopf hypersurfaces in complex hyperbolic space CH^2 with any specified value of the Hopf principal curvature less than or equal to the…

In this work, we study null hypersurfaces admitting a privileged vector field $\eta$ which is null and tangent at the hypersurface. We derive an identity that relates the deformation tensor of $\eta$ with tensor fields codifying the…

In this work we discuss stability and nondegeneracy properties of some special families of minimal hypersurfaces embedded in $\mathbb{R}^m\times \mathbb{R}^n$ with $m,n\geq 2$. These hypersurfaces are asymptotic at infinity to a fixed…

We extend the decomposition conjecture to 2d quantum field theories with a gauged $\text{Rep}(H)$ symmetry category for $H$ a finite-dimensional semisimple Hopf algebra with $\text{Rep}(G)$ trivially-acting and $\text{Vec}(\Gamma)$ the…

The first goal of this article is to give a complete classification (up to Real biholomorphisms) of Real primary Hopf surfaces $(H,s)$, and, for any such pair, to describe in detail the following naturally associated objects : the group…

Let $M$ be a real hypersurface in complex projective space. The almost contact metric structure on $M$ allows us to consider, for any nonnull real number $k$, the corresponding $k$-th generalized Tanaka-Webster connection on $M$ and,…

We set up a real entropy function $h_\Bbb{R}$ on the space $\mathcal{M}'_d$ of M\"obius conjugacy classes of real rational maps of degree $d$ by assigning to each class the real entropy of a representative $f\in\Bbb{R}(z)$; namely, the…

We prove the existence of tight frames whose elements lie on an arbitrary ellipsoidal surface within a real or complex separable Hilbert space H, and we analyze the set of attainable frame bounds. In the case where H is real and has finite…

The regular type of a real hyper-surface M in an (almost) complex manifold at some point p is the maximal contact order at p of M with germs of non singular (pseudo) holomorphic disks. The main purpose of this paper is to give two intrinsic…

Let $H \subset {\mathbb P}^n$ be a real-analytic subvariety of codimension one induced by a real-analytic curve in the Grassmannian $G(n+1,n)$. Assuming $H$ has a global defining function, we prove $H$ is Levi-flat, the closure of its…

In this paper, we classify the Hopf hypersurfaces of the complex quadric $Q^m=SO_{m+2}/(SO_2SO_m)$ ($m\geq3$) with at most five distinct constant principal curvatures. We also classify the Hopf hypersurfaces of $Q^m$ ($m=3,4,5$) with…

In this paper, we characterize the rigidity of umbilical hypersurfaces by a Serrin-type partially overdetermined problem in space forms, which generalizes the similar results in Euclidean half-space and Euclidean half-ball. Guo-Xia first…

We prove an unexpected general relation between the Jacobian syzygies of a projective hypersurface $V\subset \mathbb{P}^n$ with only isolated singularities and the nature of its singularities. This allows to establish a new method for the…

We consider the Anti-de Sitter space $\mathbb{H}^3_1$ equipped with Berger-like metrics, that deform the standard metric of $\mathbb{H}^3_1$ in the direction of the hyperbolic Hopf vector field. Helix surfaces are the ones forming a…

We use two ingredients to prove the hyperbolicity of generic hypersurfaces of sufficiently high degree and of their complements in the complex projective space. One is the pullbacks of appropriate low pole order meromorphic jet…