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It is proved, that if M is a connected, complete submanifold of a complexspace form N and each geodesic of M lies in an 1-dimensional totally geodesiccomplex submanifold of N, then M is totally geodesic in N and is a real spaceform or a complex space form.

Submanifolds of a complex space form, whose geodesics lie in 1 - dimensional complex submanifolds