The invariants of generalized $f$-transformations for almost contact metric structures

In this paper we consider such generalizations of conformal transformations for contact metric manifolds as generalized conformal transformations, $f$-transformations, generalized $f$-transformations. Components of tensor fields for almost contact metric structure are given. These components are found in A-frame. Components for the tensor of affine deformation by Riemannian connection are calculated in this paper.We study six structure tensors of almost contact metric manifold.They are not invariant under generalized conformal transformations.We consider a particular case of the generalized conformal transformation, i.e. $f$-transformation, third, fifth structure tensors are invariant under this transformation. Conditions of invariance for other structure tensors are received. The invariance of six structure tensors under generalized $f$-transformations is studied. The second structure tensor is invariant under the generalized $f$-transformation. Vanishing of third and fifth structure tensors is invariant under this transformation.We got the conditions of invariance under these transformations for first structured tensor under generalized $f$-transformation.
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