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It was shown in [15,16] that there does not exist any warped product submanifold of a Kaehler manifold such that the spherical manifold of the warped product is proper slant. In this paper, we introduce the notion of warped product submanifolds with a slant function. We show that there exists a class of nontrivial warped product submanifolds of a Kaehler manifold such that the spherical manifold is pointwise slant by giving an example and a characterization theorem. We also prove that if the warped product is mixed totally geodesic then the warping function is constant.

We introduce a special kind of almost geodesic mappings of the first type π * 1 of spaces with non-symmetric affine connections. Also, we investigate a special class of equitorsion almost geodesic mappings of type π * 1 and find some invariant geometric objects of these mappings.

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