Hessian of the natural Hermitian form on twistor spaces
- Resource Type
- Authors
- Noël Le Du; Christophe Mourougane; Guillaume Deschamps
- Source
- Bulletin de la société mathématique de France
Bulletin de la société mathématique de France, 2017, 145 (1), pp.1-27. 〈10.24033/bsmf.2729〉
Bulletin de la société mathématique de France, Société Mathématique de France, 2017, 145 (1), pp.1-27. ⟨10.24033/bsmf.2729⟩
Bulletin de la société mathématique de France, 2017, 145 (1), pp.1-27. ⟨10.24033/bsmf.2729⟩
- Subject
- Mathematics - Differential Geometry
Pure mathematics
[ MATH.MATH-CV ] Mathematics [math]/Complex Variables [math.CV]
Closed manifold
53C28
53C26
32Q45
General Mathematics
Invariant manifold
twistor space
01 natural sciences
Pseudo-Riemannian manifold
Twistor theory
symbols.namesake
Mathematics - Algebraic Geometry
High Energy Physics::Theory
FOS: Mathematics
Hermitian manifold
0101 mathematics
Complex Variables (math.CV)
hyperkähler manifold
Algebraic Geometry (math.AG)
Mathematics::Symplectic Geometry
4-dimensional Riemannian manifold
Ricci curvature
strong KT manifolds
Mathematics
quaternionic Kähler manifold
Mathematics - Complex Variables
010102 general mathematics
Mathematical analysis
Holonomy
[MATH.MATH-CV]Mathematics [math]/Complex Variables [math.CV]
Mathematics::Geometric Topology
[ MATH.MATH-AG ] Mathematics [math]/Algebraic Geometry [math.AG]
[ MATH.MATH-DG ] Mathematics [math]/Differential Geometry [math.DG]
Differential Geometry (math.DG)
[MATH.MATH-DG]Mathematics [math]/Differential Geometry [math.DG]
symbols
Twistor space
[MATH.MATH-AG]Mathematics [math]/Algebraic Geometry [math.AG]
Mathematics::Differential Geometry
- Language
- English
- ISSN
- 0037-9484
1777-568X
2102-622X
International audience; We compute the hessian of the natural Hermitian form successively on the Calabi family of a hyperkähler manifold, on the twistor space of a 4-dimensional anti-self-dual Riemannian manifold and on the twistor space of a quaternionic Kähler manifold. We show a strong convexity property of the cycle space of twistor lines on the Calabi family of a hyperkähler manifold. We also prove convexity properties of the 1-cycle space of the twistor space of a 4-dimensional anti-self-dual Einstein manifold of non-positive scalar curvature and of the 1-cycle space of the twistor space of a quaternionic Kähler manifold of non-positive scalar curvature. We check that no non-Kähler strong KT manifold occurs as such a twistor space.