A characterization of the Veronese varieties

Katsumi Nomizu
1976 Nagoya mathematical journal  
LetPm(C)be the complex projective space of dimensionm. In a previous paper [2] we have provedTHEOREM A.Let f be a Kaehlerian immersion of a connected, complete Kaehler manifold Mnof dimension n into Pm(C). If the image f(τ) of each geodesic τ in Mnlies in a complex projective line P1(C) of Pm(C), then f(Mn) is a complex projective subspace of Pm(C), and f is totally geodesic.
doi:10.1017/s0027763000017220 fatcat:65bvjcg4i5hqfoqjzhftgs3d3m