Integrability conditions of an almost quarternion manifold were studied by Yano and Ako [7]. Hamoui [1] and others have studied quaternion submanifolds of codimension 2 [1]. Vanzura [5] defined and have studied almost r- contact structure on manifolds. In this paper we have defined the Hsu-quaternion manifold and studied the submanifolds of codimension p immersed in a generalized Hsu quaternion manifold. Certain other interesting results have also been established.
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