Related papers: The CR Ahlfors derivative and a new invariant for …

It is a classical problem in algebraic geometry to characterize the algebraic subvariety by using the Gauss map. In this note, we try to develop the analogue theory in CR geometry. In particular, under some assumptions, we show that a CR…

The notion of Schwarzian derivative for locally univalent holomorphic functions on complex plane was generalized for conformal diffeomorphisms by Osgood and Stowe in 1992 [27]. We shall identify a tensor that may serve as an analogue of the…

In this paper, we study CR maps between hyperquadrics and Winkelmann hypersurfaces. Based on a previous study on the CR Ahlfors derivative of Lamel-Son and a recent result of Huang-Lu-Tang-Xiao on CR maps between hyperquadrics, we prove…

The equivariant CR minimal immersions from the round $3$-sphere $S^3$ into the complex projective space $\mathbb CP^n$ have been classified by the third author explicitly (J London Math Soc 68: 223-240, 2003). In this paper, by employing…

We compute a recently introduced geometric invariant of stricly pseudoconvex CR 3-manifolds for certain circle invariant spherical CR structures on Seifert manifolds. We give applications to the problem of filling the CR manifold by a…

This paper deals with the notion of quadratic differential in spherical CR geometry (or more generally on strictly pseudoconvex CR manifolds). We get to this notion by studying a splitting of Rumin complex and discuss its first features…

Let $(M,g)$ be a pseudo-Riemannian manifold. We propose a new approach for defining the conformal Schwarzian derivatives. These derivatives are 1-cocycles on the group of diffeomorphisms of $M$ related to the modules of linear differential…

In this article we introduce conformal Riemannian morphisms. The idea of conformal Riemannian morphism generalizes the notions of an isometric immersion, a Riemannian submersion, an isometry, a Riemannian map and a conformal Riemannian map.…

Recently continuous rational maps between real algebraic varieties have attracted the attention of several researchers. In this paper we continue the investigation of approximation properties of continuous rational maps with values in…

We construct group-invariant CR maps from the unit sphere in $\mathbb{C}^3$ and provide sharp bounds for the gap termination in this setting.

We study an analog in CR-geometry of the conformal volume of Li-Yau. In particular, to submanifolds of odd-dimensional spheres that are Legendrian or, more generally, horizontal with respect to the sphere's standard CR-structure we…

First introduced to describe surfaces embedded in $\mathbb{R}^3$, the Willmore invariant is a conformally-invariant extrinsic scalar curvature of a surface that vanishes when the surface minimizes bending and stretching. Both this invariant…

For a nonconstant holomorphic map between projective Riemann surfaces with conformal metrics, we consider invariant Schwarzian derivatives and projective Schwarzian derivatives of general virtual order. We show that these two quantities are…

We prove a smooth version of the classical Schwarz reflection principle for CR mappings between an abstract CR manifold $M$ and a generic CR manifold embedded in euclidean complex space. As a consequence of our results, we settle a…

This is the second part of a paper describing a new concept of separation of variables applied to the classical Clebsch integrable case. The quadratures obtained in Part I (also uploaded in arXiv.org) lead to a new type of the Abel map…

A chord diagram is a circle with paired points with each pair of points connected by a chord. Every generic immersed spherical curve provides a chord diagram by associating each chord with two preimages of a double point. Any two spherical…

The CR analogue of B.-Y. Chen's conjecture on pseudo biharmonic maps will be shown. Pseudo biharmonic, but not pseudo harmonic, isometric immersions with parallel pseudo mean curvature vector fields, will be characterized. Several examples…

This paper establishes a relation between two invariants of $3$-dimensional manifolds: the chromatic spherical invariant $\mathcal{K}$ and the Hennings-Kauffman-Radford invariant $\operatorname{HKR}$. We show that, for a spherical Hopf…

Combining the definition of Schwarzian derivative for conformal mappings between Riemannian manifolds given by Osgood and Stowe with that for parametrized curves in Euclidean space given by Ahlfors, we establish injectivity criteria for…

In this paper we give a survey of the constructions in math.DG/0510061 of several new invariants for CR and contact manifolds. The latter extend previous constructions of Hirachi and Boutet de Monvel. In addition, we give simple…