• Corpus ID: 17492001


  author={Weakly SELF-DUAL and K{\"a}hler Surfaces and Liviu Ornea and Mihaela Pilca},

On the uniqueness of supersymmetric AdS(5) black holes with toric symmetry

We consider the classification of supersymmetric AdS5 black hole solutions to minimal gauged supergravity that admit a torus symmetry. This problem reduces to finding a class of toric Kähler metrics

Some QCH Kahler surfaces with zero scalar curvature

In this paper we prove that some well known Kähler surfaces with zero scalar curvature are QCH Kähler. We prove that family of generalized Taub-Nut Kähler surfaces parametrized by k ∈ [−1, 1] is of

On Toric Hermitian ALF Gravitational Instantons

. We give a classification of toric, Hermitian, Ricci flat, ALF Riemannian metrics in dimension 4, including metrics with conical singularities. The only smooth examples are on one hand the hyperKähler

Globally conformally Kähler Einstein metrics on certain holomorphic bundles

  • Zhiming Feng
  • Mathematics
    Annali di Matematica Pura ed Applicata (1923 -)
  • 2022
The subject of this paper is the explicit momentum construction of complete Einstein metrics by ODE methods. Using the Calabi ansatz, further generalized by Hwang-Singer, we show that there are

Generalized orthotoric Kähler surfaces

Twisting non-shearing congruences of null geodesics, almost CR structures and Einstein metrics in even dimensions

We investigate the geometry of a twisting non-shearing congruence of null geodesics on a conformal manifold of even dimension greater than four and Lorentzian signature. We give a necessary and

An Obata-type characterization of Calabi metrics on line bundles

We characterize those complete K{a}hler manifolds supporting a nonconstant real-valued function with critical points whose Hessian is complex linear, has pointwise two eigenvalues and whose gradient

Conformally Kähler, Einstein–Maxwell metrics on Hirzebruch surfaces

In this note, we prove that a special family of Killing potentials on certain Hirzebruch complex surfaces, found by Futaki and Ono [ 18 ], gives rise to new conformally Kähler, Einstein–Maxwell

Levi–Kähler reduction of CR structures, products of spheres, and toric geometry

We study CR geometry in arbitrary codimension, and introduce a process, which we call the Levi-Kahler quotient, for constructing Kahler metrics from CR structures with a transverse torus action. Most

Invariant scalar-flat Kähler metrics on O(-ℓ)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathcal {O} (- \ell )$$\

  • Bollettino dell'Unione Matematica Italiana
  • 2018



Kaehler structures on toric varieties

1. Let (X, ω) be a compact connected 2w-dimensional manifold, and let (1.1) τ: T -+Όifί(X, ω) be an effective Hamiltonian action of the standard w-torus. Let φ: X —> R be its moment map. The image,

The Geometry of Weakly Self-dual Kähler Surfaces

We study Kähler surfaces with harmonic anti-self-dual Weyl tensor. We provide an explicit local description, which we use to obtain the complete classification in the compact case. We give new

Einstein-Weyl geometry, the Bach tensor and conformal scalar curvature.

A conformal manifold with compatible torsion-free connection is said to be EinsteinWeyl if the symmetrised Ricci tensor of the conformal connection is proportional to a representative metric. This is

Conformal Killing forms on Riemannian manifolds

Conformal Killing forms are a natural generalization of conformal vector fields on Riemannian manifolds. They are defined as sections in the kernel of a conformally invariant first order differential

Hamiltonian 2-forms in Kahler geometry, I

We introduce the notion of a hamiltonian 2-form on a Kähler man-ifold and obtain a complete local classification. This notion appears to play a pivotal role in several aspects of Kähler geometry. In


A (symplectic) toric variety X, of real dimension 2n, is completely determined by its moment polytope Δ ⊂ ℝn. Recently Guillemin gave an explicit combinatorial way of constructing "toric" Kahler

Selfdual Einstein Metrics with Torus Symmetry

It is well-known that any 4-dimensional hyperkahler metric with two commuting Killing fields may be obtained explicitly, via the Gibbons-Hawking Ansatz, from a harmonic function invariant under a