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In this paper we initiate the study of submanifolds of almost hypercomplexmanifolds with Hermitian and Norden metrics. Object of investigations areholomorphic submanifolds of the hypercomplex manifolds which are locallyconformally equivalent to the hyper-K\"ahler manifolds of the considered type.Necessary and sufficient conditions the investigated holomorphic submanifoldsto be totally umbilical or totally geodesic are obtained. Examples of theexamined submanifolds are constructed.

Holomorphic submanifolds of some hypercomplex manifolds with Hermitian and Norden metrics