| In this paper, we mainly study the totally real pseudo-umbilical sub-manifolds of a complex projective space: We discuss how to construct themand give the examples. Some pinching theorems about totally real pseudo-umbilical submanifolds with parallel mean curvature vector becoming totallyreal and totally umbilical submanifolds are obtained by choosing a suitableframe ?eld. Finally we prove that two types of totally real pseudo-umbilicalsubmanifolds with ?at normal bundle must be minimal.
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