On the cone of strong Kähler with torsion metrics
type: Item
instance of: scholarly article
title: On the cone of strong Kähler with torsion metrics
zbMATH Open document ID: 1409.53061
author: Michele Maschio
published in: Annali di Matematica Pura ed Applicata. Serie Quarta
publication date: 2017-11-24T00:00:00Z
review text: This paper examines special metrics on compact complex manifolds, focusing on the notion of super strong Kähler with torsion metrics. This condition is related to the strong Kähler with torsion one in the same manner as the strongly Gauduchon condition is related to the Gauduchon one. The author provides sufficient and necessary conditions so that evert strong Kähler with torsion metric on a compact manifold is super strong Kähler with torsion. It is also shown that these conditions are verified on compact complex manifolds satisfying the \(\partial\overline{\partial}\)-lemma but not on 6-dimensional compact complex nilmanifolds.
reviewed by: Martin Chuaqui
Mathematics Subject Classification ID: 53C55
Mathematics Subject Classification ID: 15B48
Mathematics Subject Classification ID: 15B57
Mathematics Subject Classification ID: 32Q57
zbMATH DE Number: 6812664
zbMATH Keywords: MSTK metric
zbMATH Keywords: complex manifold
zbMATH Keywords: super strong Kähler metric
zbMATH Keywords: torsion cone
zbMATH Keywords: exact sequence
MaRDI profile type: Publication
full work available at URL: s10231-017-0654-3
OpenAlex ID: W2596529215
cites work: Degree of non-Kählerianity for 6-dimensional nilmanifolds
cites work: Bott-Chern cohomology of solvmanifolds
cites work: On small deformations of balanced manifolds
cites work: On the metric structure of non-Kähler complex surfaces
cites work: Invariant complex structures on 6-nilmanifolds: classification, Frölicher spectral sequence and special Hermitian metrics
cites work: Special metrics on compact complex manifolds
cites work: Properties of manifolds with skew-symmetric torsion and special holonomy
cites work: Families of strong KT structures in six dimensions
cites work: On blow-ups and cohomology of almost complex manifolds
cites work: Q4136133
cites work: On the Bott-Chern cohomology and balanced Hermitian nilmanifolds
cites work: On the existence of special metrics in complex geometry
cites work: Hermitian structures on six-dimensional nilmanifolds
cites work: Deformation openness and closedness of various classes of compact complex manifolds; Examples
cites work: A Parabolic Flow of Pluriclosed Metrics
cites work: Q3719047
Wikidata QID: Q126122294
DOI: 10.1007/S10231-017-0654-3
Recommended article: Deformations of strong Kähler with torsion metrics
Recommended article: Blow-ups and resolutions of strong Kähler with torsion metrics
Recommended article: A remark on conical Kähler-Einstein metrics
Recommended article: Strong Kähler with torsion structures from almost contact manifolds
Recommended article: On cohomological and formal properties of strong Kähler with torsion and astheno-Kähler metrics
Recommended article: Toric Kähler-Einstein metrics and convex compact polytopes
Recommended article: Vanishing theorems on \((\ell | k)\)-strong Kähler manifolds with torsion
Recommended article: Conical Kähler-Einstein metrics revisited
Recommended article: Kähler Metrics with Cone Singularities Along a Divisor
Recommended article: On toric locally conformally Kähler manifolds
description: scientific article; zbMATH DE number 6812664