Starting from the definition of generalized Riemannian space (GR N ) [5], in which a non-symmetric basic tensor g ij is introduced, in the present paper a generalized Kählerian space GK 2 N of the second kind is defined, as a GR N with almost complex structure F h i , that is covariantly constant with respect to the second kind of covariant derivative (equation (2.3)).We observe hollomorphically projective mapping of the spaces GK 2 N and GK 2 N with invariant complex structure. Also, we consider equitorsion geodesic mapping between these two spaces, and for them we find invariant geometric objects.
We investigate a second order infinitesimal bending of curves in a three-dimensional Euclidean space in this paper. We give the necessary and sufficient conditions for the vector fields to be infinitesimal bending fields of the corresponding order, as well as explicit formulas which determine these fields. We examine the first and the second variation of some geometric magnitudes which describe a curve, specially a change of the curvature. Two illustrative examples (a circle and a helix) are studied not only analytically but also by drawing curves using computer program Mathematica.
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