Results 31 to 40 of about 1,101 (109)

Curvature of quaternionic skew‐Hermitian manifolds and bundle constructions

Mathematische Nachrichten, Volume 298, Issue 1, Page 87-112, January 2025.
Abstract This paper is devoted to a description of the second‐order differential geometry of torsion‐free almost quaternionic skew‐Hermitian manifolds, that is, of quaternionic skew‐Hermitian manifolds (M,Q,ω)$(M, Q, \omega)$. We provide a curvature characterization of such integrable geometric structures, based on the holonomy theory of symplectic ...
Ioannis Chrysikos, Vicente Cortés, Jan Gregorovič   +2 more
wiley   +1 more source

Special Kähler geometry and holomorphic Lagrangian fibrations

Comptes Rendus. Mathématique
Given a holomorphic Lagrangian fibration of a compact hyperkähler manifold, we use the differential geometry of the special Kähler metric that exists on the base away from the discriminant locus, and show that the pullback of the tangent bundle of the ...
Li, Yang, Tosatti, Valentino
doaj   +1 more source

Characteristic foliations — A survey

Bulletin of the London Mathematical Society, Volume 56, Issue 7, Page 2231-2249, July 2024.
Abstract This is a survey article, with essentially complete proofs, of a series of recent results concerning the geometry of the characteristic foliation on smooth divisors in compact hyperkähler manifolds, starting with work by Hwang–Viehweg, but also covering articles by Amerik–Campana and Abugaliev.
Fabrizio Anella, Daniel Huybrechts
wiley   +1 more source

Yang-Mills instantons in Kaehler spaces with one holomorphic isometry

, 2017
We consider self-dual Yang-Mills instantons in 4-dimensional Kaehler spaces with one holomorphic isometry and show that they satisfy a generalization of the Bogomol'nyi equation for magnetic monopoles on certain 3-dimensional metrics.
Chimento, Samuele, Ortin, Tomas, Ruiperez, Alejandro   +2 more
core   +2 more sources

Subquadratic harmonic functions on Calabi‐Yau manifolds with maximal volume growth

Communications on Pure and Applied Mathematics, Volume 77, Issue 6, Page 3080-3106, June 2024.
Abstract On a complete Calabi‐Yau manifold M$M$ with maximal volume growth, a harmonic function with subquadratic polynomial growth is the real part of a holomorphic function. This generalizes a result of Conlon‐Hein. We prove this result by proving a Liouville‐type theorem for harmonic 1‐forms, which follows from a new local L2$L^2$ estimate of the ...
Shih‐Kai Chiu
wiley   +1 more source

Limits of Riemannian 4-manifolds and the symplectic geometry of their twistor spaces

, 2016
The twistor space of a Riemannian 4-manifold carries two almost complex structures, $J_+$ and $J_-$, and a natural closed 2-form $\omega$. This article studies limits of manifolds for which $\omega$ tames either $J_+$ or $J_-$.
Fine, Joel
core   +1 more source

Gravitational instantons with quadratic volume growth

Journal of the London Mathematical Society, Volume 109, Issue 4, April 2024.
Abstract There are two known classes of gravitational instantons with quadratic volume growth at infinity, known as type ALG$\operatorname{ALG}$ and ALG∗$\operatorname{ALG}^*$. Gravitational instantons of type ALG$\operatorname{ALG}$ were previously classified by Chen–Chen.
Gao Chen, Jeff Viaclovsky
wiley   +1 more source

On numerically trivial automorphisms of compact hyperkähler manifolds of dimension 4 [PDF]

, 2023
Chen Jiang, Wenfei Liu
openalex   +1 more source

Closed 3‐forms in five dimensions and embedding problems

Journal of the London Mathematical Society, Volume 109, Issue 4, April 2024.
Abstract We consider the question if a five‐dimensional manifold can be embedded into a Calabi–Yau manifold of complex dimension 3 such that the real part of the holomorphic volume form induces a given closed 3‐form on the 5‐manifold. We define an open set of 3‐forms in dimension five which we call strongly pseudoconvex, and show that for closed ...
Simon Donaldson, Fabian Lehmann
wiley   +1 more source

Abundance for varieties with many differential forms

, 2018
We prove that the abundance conjecture holds on a variety $X$ with mild singularities if $X$ has many reflexive differential forms with coefficients in pluricanonical bundles, assuming the Minimal Model Program in lower dimensions.
Lazić, Vladimir, Peternell, Thomas
core   +1 more source