YE, Y-G, EXTREMAL RAYS AND NULL GEODESICS ON A COMPLEX CONFORMAL MANIFOLD,
International Journal of Mathematics, vol. 05 no. 01
(February, 1994),
pp. 141-168, World Scientific Pub Co Pte Lt
(last updated on 2021/07/22)
Abstract:
A holomorphic conformal structure on a complex manifold X is an everywhere non-degenerate section [Formula: see text] for some line bundle N. In this paper, we show that if X is a projective complex n-dimensional manifold with non-numerically effective Kx and admits a holomorphic conformal structure, then X ≅ ℚn. This in particular answers affirmatively a question of Kobayashi and Ochiai. They asked if the same holds assuming c1 (X) > 0. As a consequence, we also show that any projective conformal manifold with an immersed rational null geodesic is necessarily a smooth hyperquadric ℚn.