Induced transformations for almost Hermitian structure of linear extensions

Induced transformation of almost Hermitian structure for linear extension of the manifold with almost contact metric structure was considered in this paper. We got formulas for induced transformation of almost Hermitian structure for linear extension of the smooth manifold with almost contact metric structure. There exist four equations for the Gray–Hervella's classification of the smooth manifolds with almost Hermitian structures. In this paper we studied invariance of these equations. One equation is invariant. The conditions of invariance for three other equations were got in this paper. These equations defined sixteen classes of the smooth manifolds with almost Hermitian structure. In this paper we studied invariance for these classes. One class is invariant. Six classes are invariant if and only if exterior differential of function of induced transformation is contained in the second fundamental distribution. Other classes are invariant if and only if the function of induced transformation is constant.
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