Summary
The metric compound structure of rank r is an obstructed structure of an induced structure on a real submanifold in an almost Hermitian manifold. In this paper we deal with a submanifold with metric compound structure of rank 2 in a Kaehlerian manifold and we classify it under some suitable conditions. Namely it is a standard sphere or neither Einstein nor conformally flat.
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Yamaguchi, S., Nemoto, H. & Jun, J.B. Submanifolds of Kaehlerian manifold with a metric compound structure of rank 2. Annali di Matematica pura ed applicata 147, 105–116 (1987). https://doi.org/10.1007/BF01762413
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DOI: https://doi.org/10.1007/BF01762413