Results 1 to 10 of about 2,185 (102)

Canonical metrics on generalized Hartogs triangles

Comptes rendus. Mathematique, 2022
This paper is concerned with the canonical metrics on generalized Hartogs triangles. As main contributions, we first show the existence of a Kähler–Einstein metric on generalized Hartogs triangles.
Enchao Bi, Z. Hou
semanticscholar   +1 more source

Hessian equations of Krylov type on compact Hermitian manifolds

Open Mathematics, 2022
In this article, we are concerned with the equations of Krylov type on compact Hermitian manifolds, which are in the form of the linear combinations of the elementary symmetric functions of a Hermitian matrix.
Zhou Jundong, Chu Yawei
doaj   +1 more source

Deformations of Strong Kähler with torsion metrics

Complex Manifolds, 2021
Existence of strong Kähler with torsion metrics, shortly SKT metrics, on complex manifolds has been shown to be unstable under small deformations.
Piovani Riccardo, Sferruzza Tommaso
doaj   +1 more source

Locally conformally balanced metrics on almost abelian Lie algebras

Complex Manifolds, 2021
We study locally conformally balanced metrics on almost abelian Lie algebras, namely solvable Lie algebras admitting an abelian ideal of codimension one, providing characterizations in every dimension. Moreover, we classify six-dimensional almost abelian
Paradiso Fabio
doaj   +1 more source

Local Classification of Conformally‐Einstein Kähler Metrics in Higher Dimensions [PDF]

, 2002
The requirement that a (non‐Einstein) Kähler metric in any given complex dimension m > 2 be almost‐everywhere conformally Einstein turns out to be much more restrictive, even locally, than in the case of complex surfaces. The local biholomorphic‐isometry
A. Derdzinski, G. Maschler
semanticscholar   +1 more source

Deformations of astheno-Kähler metrics

Complex Manifolds, 2023
The property of admitting an astheno-Kähler metric is not stable under the action of small deformations of the complex structure of a compact complex manifold.
Sferruzza Tommaso
doaj   +1 more source

\'Etale triviality of finite equivariant vector bundles [PDF]

Épijournal de Géométrie Algébrique, 2021
Let H be a complex Lie group acting holomorphically on a complex analytic space X such that the restriction to X_{\mathrm{red}} of every H-invariant regular function on X is constant.
Indranil Biswas, Peter O'Sullivan
doaj   +1 more source

Hamiltonian Stationary Tori in the Complex Projective Plane [PDF]

, 2003
Hamiltonian stationary Lagrangian surfaces are Lagrangian surfaces in a four‐dimensional Kähler manifold which are critical points of the area functional for Hamiltonian infinitesimal deformations.
Fr'ed'eric H'elein, P. Romon
semanticscholar   +1 more source

A Remark on Kähler Metrics of Constant Scalar Curvature on Ruled Complex Surfaces [PDF]

, 2004
In this paper we point out how some recent developments in the theory of constant scalar curvature Kähler metrics can be used to clarify the existence issue for such metrics in the special case of (geometrically) ruled complex surfaces.
V. Apostolov, Christina W. Tønnesen-Friedman   +1 more
semanticscholar   +1 more source

On the Hermitian structures of the sequence of tangent bundles of an affine manifold endowed with a Riemannian metric

Complex Manifolds, 2022
Let (M, ∇, 〈, 〉) be a manifold endowed with a flat torsionless connection r and a Riemannian metric 〈, 〉 and (TkM)k≥1 the sequence of tangent bundles given by TkM = T(Tk−1M) and T1M = TM. We show that, for any k ≥ 1, TkM carries a Hermitian structure (Jk,
Boucetta Mohamed
doaj   +1 more source