Orthogonal complex structures on certain Riemannian 6-manifolds
type: Item
instance of: scholarly article
title: Orthogonal complex structures on certain Riemannian 6-manifolds
zbMATH Open document ID: 0964.53032
DOI: 10.1016/S0926-2245(99)00041-8
published in: Differential Geometry and its Applications
publication date: 2001-06-28T00:00:00Z
review text: Let \(M\) be the Hermitian-symmetric space \({\mathbb P}^1{\mathbb C}\times {\mathbb P}^1{\mathbb C}\times{\mathbb P}^1{\mathbb C}\) or the flag manifold \[ F_{1 2}= U(3)/(U(1)\times U(1)\times U(1)) \] equipped with any left invariant metric. It is shown that any integrable almost complex structure on \(M\) which is compatible with both, the Riemann metric and the orientation of \(M\), must be invariant, even if the integrable almost complex structure is only locally defined. Moreover, a compact Kähler-Einstein spin 6-manifold whose holomorphic sectional curvature is non-negative and not identically zero, must be one of the two examples above, if it admits another compatible Kähler structure.
Mathematics Subject Classification ID: 53C30
Mathematics Subject Classification ID: 14J30
Mathematics Subject Classification ID: 53C55
Mathematics Subject Classification ID: 53C27
zbMATH DE Number: 1454703
zbMATH Keywords: orthogonal complex structures
zbMATH Keywords: Fano 3-fold
zbMATH Keywords: harmonic map
zbMATH Keywords: twistor space
Wikidata QID: Q115337395
author: Vestislav Apostolov
author: Gueo Grantcharov
author: Stefan Ivanov
reviewed by: Stefan Helmke
MaRDI profile type: Publication
full work available at URL: s0926-2245(99)00041-8
OpenAlex ID: W1967840818
description: scientific article; zbMATH DE number 1454703