Related papers: Weil-Petersson geometry for families of hyperbolic…

We develop the properties of Weyl geometry, beginning with a review of the conformal properties of Riemannian spacetimes. Decomposition of the Riemann curvature into trace and traceless parts allows an easy proof that the Weyl curvature…

We prove topological transitivity for the Weil Petersson geodesic flow for two-dimensional moduli spaces of hyperbolic structures. Our proof follows a new approach that exploits the density of singular unit tangent vectors, the geometry of…

We study deformations of complex hyperbolic surfaces which furnish the simplest examples of: (i) negatively curved K\"ahler manifolds and (ii) negatively curved Riemannian manifolds not having {\it constant} curvature. Although such complex…

We present a computational approach to general hyperelliptic Riemann surfaces in Weierstrass normal form. The surface is either given by a list of the branch points, the coefficients of the defining polynomial or a system of cuts for the…

We define an ending lamination for a Weil-Petersson geodesic ray. Despite the lack of a natural visual boundary for the Weil-Petersson metric, these ending laminations provide an effective boundary theory that encodes much of its asymptotic…

We extend a theorem of Masur and Wolf which says that given a hyperbolic surface S, every isometry of the Teichmuller space for S with the Weil-Petersson metric is induced by an element of the mapping class group for S. Our argument handles…

In this paper we study sectional curvature of invariant hyper-Hermitian metrics on simply connected 4-dimensional real Lie groups admitting invariant hypercomplex structure. We give the Levi-Civita connections and explicit formulas for…

Assuming the stability of soliton surfaces of vanishing Ricci sectional curvature of soliton metric in the nonholonomic frame, we find a solution for the metric in the approximation of weak constant torsion curves with constant Frenet…

We collect some classical results on the versal families of ordinary compact Riemann surfaces needed in `Versal Families of Compact Super Riemann Surfaces'.

We consider classical curvature flows: 1-parameter families of convex embeddings of the 2-sphere into Euclidean 3-space which evolve by an arbitrary (non-homogeneous) function of the radii of curvature. The associated flow of the radii of…

We study hyperbolic polyhedral surfaces with faces isometric to regular hyperbolic polygons satisfying that the total angles at vertices are at least $2\pi.$ The combinatorial information of these surfaces is shown to be identified with…

We classify hypersurfaces with rotational symmetry and positive constant $r$-th mean curvature in $\mathbb H^n \times \mathbb R$. Specific constant higher order mean curvature hypersurfaces invariant under hyperbolic translation are also…

We show that the evolution of isoparametric hypersurfaces of Riemannian manifolds by the mean curvature flow is given by a reparametrization of the parallel family in short time, as long as the uniqueness of the mean curvature flow holds…

We approach the study of totally real immersions of smooth manifolds into holomorphic Riemannian space forms of constant sectional curvature -1. We introduce a notion of first and second fundamental form, we prove that they satisfy a…

We study rotational hypersurfaces with constant Gauss-Kronecker curvature. We solve the ODE for the generating curves of such hypersurfaces and analyze several geometric properties of such hypersurfaces. In particular, we discover a class…

In this paper we examine different aspects of the geometry of closed conformal vector fields on Riemannian manifolds. We begin by getting obstructions to the existence of closed conformal and nonparallel vector fields on complete manifolds…

We study Levi-flat real analytic hypersurfaces with singularities. We prove that the Levi foliation on the regular part of the hypersurface can be holomorphically extended, in a suitable sense, to neighbourhoods of singular points.

All spherically symmetric Riemannian metrics of constant scalar curvature in any dimension can be written down in a simple form using areal coordinates. All spherical metrics are conformally flat, so we search for the conformally flat…

Weingarten surfaces are those whose principal curvatures satisfy a functional relation, whose set of solutions is called the curvature diagram or the W-diagram of the surface. Making use of the notion of geometric linear momentum of a plane…

Considering Riemannian submersions, we find necessary and sufficient conditions for when sub-Riemannian normal geodesics project to curves of constant first geodesic curvature or constant first and vanishing second geodesic curvatures. We…