Displaying similar documents to “On almost geodesic mappings of the type π 1 of Riemannian spaces preserving a system n -orthogonal hypersurfaces”

Geodesic mapping onto Kählerian spaces of the first kind

Milan Zlatanović, Irena Hinterleitner, Marija Najdanović (2014)

Czechoslovak Mathematical Journal

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In the present paper a generalized Kählerian space 𝔾 𝕂 1 N of the first kind is considered as a generalized Riemannian space 𝔾ℝ N with almost complex structure F i h that is covariantly constant with respect to the first kind of covariant derivative. Using a non-symmetric metric tensor we find necessary and sufficient conditions for geodesic mappings f : 𝔾ℝ N → 𝔾 𝕂 ¯ 1 N with respect to the four kinds of covariant derivatives. These conditions have the form of a closed system of partial differential equations in covariant...

On special almost geodesic mappings of type π 1 of spaces with affine connection

Vladimir Berezovskij, Josef Mikeš (2004)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

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N. S. Sinyukov [5] introduced the concept of an of a space A n with an affine connection without torsion onto A ¯ n and found three types: π 1 , π 2 and  π 3 . The authors of [1] proved completness of that classification for n > 5 .By definition, special types of mappings π 1 are characterized by equations P i j , k h + P i j α P α k h = a i j δ k h , where P i j h ≡ Γ ¯ i j h - Γ i j h is the deformation tensor of affine connections of the spaces A n and A ¯ n .In this paper geometric objects which preserve these mappings are found and also closed classes of such spaces are described. ...