Displaying similar documents to “Conformally geodesic mappings satisfying a certain initial condition”

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. ...

On geodesic mappings preserving the Einstein tensor

Olena E. Chepurna, Volodymyr A. Kiosak, Josef Mikeš (2010)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

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In this paper there are discussed the geodesic mappings which preserved the Einstein tensor. We proved that the tensor of concircular curvature is invariant under Einstein tensor-preserving geodesic mappings.

On F 2 ε -planar mappings of (pseudo-) Riemannian manifolds

Irena Hinterleitner, Josef Mikeš, Patrik Peška (2014)

Archivum Mathematicum

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We study special F -planar mappings between two n -dimensional (pseudo-) Riemannian manifolds. In 2003 Topalov introduced P Q ε -projectivity of Riemannian metrics, ε ≠ 1 , 1 + n . Later these mappings were studied by Matveev and Rosemann. They found that for ε = 0 they are projective. We show that P Q ε -projective equivalence corresponds to a special case of F -planar mapping studied by Mikeš and Sinyukov (1983) and F 2 -planar mappings (Mikeš, 1994), with F = Q . Moreover, the tensor P is derived from the tensor Q and...

Uniqueness of the stereographic embedding

Michael Eastwood (2014)

Archivum Mathematicum

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The standard conformal compactification of Euclidean space is the round sphere. We use conformal geodesics to give an elementary proof that this is the only possible conformal compactification.