## 22 Citations

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

- Physics
- 2022

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

- Mathematics
- 2022

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

- MathematicsCommunications in Mathematical Physics
- 2022

. 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

- MathematicsAnnali 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…

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

- MathematicsAnnali di Matematica Pura ed Applicata (1923 -)
- 2021

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

- Mathematics, Computer Science
- 2020

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

- Mathematics
- 2020

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

- MathematicsMathematical Research Letters
- 2020

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

## References

SHOWING 1-10 OF 24 REFERENCES

### Kaehler structures on toric varieties

- Mathematics
- 1994

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

- MathematicsCompositio Mathematica
- 2003

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.

- Mathematics, Physics
- 1993

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

- Mathematics
- 2002

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

- Mathematics
- 2002

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…

### KÄHLER GEOMETRY OF TORIC VARIETIES AND EXTREMAL METRICS

- Mathematics
- 1997

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

- Mathematics
- 2001

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…