Journal of the
Korean Mathematical Society JKMS

It is well known that the twistor, section of twistor space, classify the orthogonal almost complex structure on even dimensional Riemannian manifold $(X, g)$. We will show that existence of a harmonic and anti-holomorphic twistor is equivalent to having a symplectic structure on $(X,g)$.

Keywords: twistor space, pure spinor, symplectic structure

MSC numbers: 53D05, 53C28