Abstract
In this paper we prove that if M is a J-invariant sub-manifold of codimension 2 in a complex projective space <TEX>$P_{n+1}(C)$</TEX>, and the second fundamental tensor is cyclic-parallel or M has harmonic curvature, then M is locally complex quadric Q<TEX>$_n$</TEX>(C) or P<TEX>$_n$</TEX>(C).
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