Apostolov, V, Grantcharov, G, Ivanov, S. (1998). Hermitian Structures on Twistor Spaces
. ANNALS OF GLOBAL ANALYSIS AND GEOMETRY, 16(3), 291-308. 10.1023/A:1006548030918
Apostolov, V, Grantcharov, G, Ivanov, S. (1998). Hermitian Structures on Twistor Spaces
. ANNALS OF GLOBAL ANALYSIS AND GEOMETRY, 16(3), 291-308. 10.1023/A:1006548030918
The paper contains description of the orthogonal complex structures with respect to the natural 1-parameter family of Riemannian metrics on the (negative) twistor space over a self-dual Einstein Riemannian 4-manifold. We prove that if the twistor space of a compact self-dual Einstein 4-manifold admits more than one orthogonal complex structure then the 4-manifold has a Kähler structure. Considering the flag manifold F1,2 which is the twistor space of CP2 endowed with the Fubini-Study metric, we obtain that any invariant Einstein metric on F1,2 admits even locally exactly three orthogonal complex structures which are the invariant ones.
