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We study n-dimensional totally real minimal submanifolds M immersed in complex space forms M˜n(c) for c≤0. We prove that M is totally geodesic if the L2p-norm of the second fundamental form is finite for some p∈R. We also derive vanishing results for the space of harmonic forms on such submanifolds.
Cuong et al. (Thu,) studied this question.
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