TY - JOUR
T1 - The Einstein-Weyl equations in complex and quaternionic geometry
AU - Pedersen, Henrik
AU - Poon, Yat Sun
AU - Swann, Andrew
PY - 1993
Y1 - 1993
N2 - Einstein-Weyl manifolds with compatible complex structures are shown to be given as torus bundles on Kähler-Einstein manifolds, extending known results on locally conformal Kähler manifolds. The Weyl structure is derived from a Ricci-flat metric constructed by Calabi on the canonical bundle of the Kähler-Einstein manifold. Similar questions are addressed when the Weyl geometry admits compatible hypercomplex or quaternionic structures.
AB - Einstein-Weyl manifolds with compatible complex structures are shown to be given as torus bundles on Kähler-Einstein manifolds, extending known results on locally conformal Kähler manifolds. The Weyl structure is derived from a Ricci-flat metric constructed by Calabi on the canonical bundle of the Kähler-Einstein manifold. Similar questions are addressed when the Weyl geometry admits compatible hypercomplex or quaternionic structures.
KW - generalised Hopf structures
KW - Hermitian-Einstein-Weyl geometry
KW - Kähler-Einstein metrics
KW - quaternionic structures
UR - http://www.scopus.com/inward/record.url?scp=0000845575&partnerID=8YFLogxK
U2 - 10.1016/0926-2245(93)90009-P
DO - 10.1016/0926-2245(93)90009-P
M3 - Journal article
AN - SCOPUS:0000845575
SN - 0926-2245
VL - 3
SP - 309
EP - 321
JO - Differential Geometry and Its Applications
JF - Differential Geometry and Its Applications
IS - 4
ER -