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On holomorphically projective mappings onto Kählerian spaces

Mikeš, Josef; Pokorná, Olga — 2002

Proceedings of the 21st Winter School "Geometry and Physics"

The main result of this paper determines a system of linear partial differential equations of Cauchy type whose solutions correspond exactly to holomorphically projective mappings of a given equiaffine space onto a Kählerian space. The special case of constant holomorphic curvature is also studied.

$T$ -semisymmetric spaces and concircular vector fields

Mikeš, Josef; Rachůnek, Lukáš — 2002

Proceedings of the 21st Winter School "Geometry and Physics"

On almost geodesic mappings of the type $π_{1}$ of Riemannian spaces preserving a system $n$ -orthogonal hypersurfaces

Berezovskij, Vladimir; Mikeš, Josef — 1999

Proceedings of the 18th Winter School "Geometry and Physics"

On some relations between curvature and metric tensors in Riemannian spaces

Mikeš, Josef; Laitochová, Jitka; Pokorná, Olga — 2000

Proceedings of the 19th Winter School "Geometry and Physics"

The paper generalizes results of and [Dokl. Akad. Nauk, Ross. Akad. Nauk 351, No. 3, 295-296 (1996; Zbl 0895.53038) and Sib. Mat. Zh. 39, No. 4, 1005-1012 (1998; Zbl 0913.53019)] on the existence and uniqueness of a Riemannian metric on a domain in $ℝ^{n}$ given prescribed values for some of the components of the Riemann curvature tensor and initial values of the metric and its partial derivatives. The authors establish the construction (existence and uniqueness) of a metric tensor $g_{i j}$ in a semigeodesic...

On 4-planar mapping of special almost antiquaternionic spaces

Bělohlávková, Jana; Mikeš, Josef; Pokorná, Olga — 2001

Proceedings of the 20th Winter School "Geometry and Physics"

On holomorphically projective mappings from equiaffine symmetric and recurrent spaces onto Kählerian spaces

Škodová, Marie; Mikeš, Josef; Pokorná, Olga — 2005

Proceedings of the 24th Winter School "Geometry and Physics"

On the theory of the 4-quasiplanar mappings of almost quaternionic spaces

Mikeš, Josef; Němčíková, Jana; Pokorná, Olga — 1998

Proceedings of the 17th Winter School "Geometry and Physics"

Authors’ abstract: “4-quasiplanar mappings of almost quaternionic spaces with affine connection without torsion are investigated. Geometrically motivated definitions of these mappings are presented. Based an these definitions, fundamental forms of these mappings are found, which are equivalent to the forms of 4-quasiplanar mappings introduced a priori by [Sov. Math. 30, 100-104 (1986; Zbl 0602.53029)]”.

On almost geodesic mappings $π_{2} (e)$ onto Riemannian spaces

Mikeš, Josef; Pokorná, Olga; Starko, Galina — 2004

Proceedings of the 23rd Winter School "Geometry and Physics"

$F$ -Планарные преобразования пространств аффинной связности

Josef Mikeš — 1991

Archivum Mathematicum

Conformally geodesic mappings satisfying a certain initial condition

Hana Chudá; Josef Mikeš — 2011

Archivum Mathematicum

In this paper we study conformally geodesic mappings between pseudo-Riemannian manifolds $(M, g)$ and $(\bar{M}, \bar{g})$ , i.e. mappings $f : M \to \bar{M}$ satisfying $f = f_{1} \circ f_{2} \circ f_{3}$ , where $f_{1}, f_{3}$ are conformal mappings and $f_{2}$ is a geodesic mapping. Suppose that the initial condition $f^{*} \bar{g} = k g$ is satisfied at a point $x_{0} \in M$ and that at this point the conformal Weyl tensor does not vanish. We prove that then $f$ is necessarily conformal.

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

N. S. Sinyukov [5] introduced the concept of an of a space $A_{n}$ with an affine connection without torsion onto ${\bar{A}}_{n}$ 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 $P_{i j}^{h} \equiv {\bar{Γ}}_{i j}^{h} - Γ_{i j}^{h}$ is the deformation tensor of affine connections of the spaces $A_{n}$ and ${\bar{A}}_{n}$ .In this paper geometric objects which preserve these mappings are found and also closed classes of such spaces are described.

On tensor fields semiconjugated with torse-forming vector fields

Lukáš Rachůnek; Josef Mikeš — 2005

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

The paper deals with tensor fields which are semiconjugated with torse-forming vector fields. The existence results for semitorse-forming vector fields and for convergent vector fields are proved.

On a classification of almost geodesic mappings of affine connection spaces

Vladimir Berezovskij; Josef Mikeš — 1996

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

Shells of monotone curves

Josef Mikeš; Karl Strambach — 2015

Czechoslovak Mathematical Journal

We determine in $ℝ^{n}$ the form of curves $C$ corresponding to strictly monotone functions as well as the components of affine connections $\nabla$ for which any image of $C$ under a compact-free group $Ω$ of affinities containing the translation group is a geodesic with respect to $\nabla$ . Special attention is paid to the case that $Ω$ contains many dilatations or that $C$ is a curve in $ℝ^{3}$ . If $C$ is a curve in $ℝ^{3}$ and $Ω$ is the translation group then we calculate not only the components of the curvature and the Weyl tensor but...

On holomorphically projective mappings from manifolds with equiaffine connection onto Kähler manifolds

Irena Hinterleitner; Josef Mikeš — 2013

Archivum Mathematicum

In this paper we study fundamental equations of holomorphically projective mappings from manifolds with equiaffine connection onto (pseudo-) Kähler manifolds with respect to the smoothness class of connection and metrics. We show that holomorphically projective mappings preserve the smoothness class of connections and metrics.

On $F_{2}^{ε}$ -planar mappings of (pseudo-) Riemannian manifolds

Irena Hinterleitner; Josef Mikeš; Patrik Peška — 2014

Archivum Mathematicum

We study special $F$ -planar mappings between two $n$ -dimensional (pseudo-) Riemannian manifolds. In 2003 Topalov introduced $P Q^{ε}$ -projectivity of Riemannian metrics, $ε \neq 1, 1 + n$ . 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 the non-zero...

Equipping distributions for linear distribution

Marina F. Grebenyuk; Josef Mikeš — 2007

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

In this paper there are discussed the three-component distributions of affine space $A_{n + 1}$ . Functions ${ℳ^{σ}}$ , which are introduced in the neighborhood of the second order, determine the normal of the first kind of $ℋ$ -distribution in every center of $ℋ$ -distribution. There are discussed too normals ${𝒵^{σ}}$ and quasi-tensor of the second order ${𝒮^{σ}}$ . In the same way bunches of the projective normals of the first kind of the $ℳ$ -distributions were determined in the differential neighborhood of the second and third order.

Our aim is to study the principal bundles determined by the algebra of quaternions in the projective model. The projectivization of the conformal model of the Hopf fibration is considered as example.

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Currently displaying 1 – 20 of 25

On holomorphically projective mappings onto Kählerian spaces

$T$ -semisymmetric spaces and concircular vector fields

On almost geodesic mappings of the type $π_{1}$ of Riemannian spaces preserving a system $n$ -orthogonal hypersurfaces

On some relations between curvature and metric tensors in Riemannian spaces

On 4-planar mapping of special almost antiquaternionic spaces

On holomorphically projective mappings from equiaffine symmetric and recurrent spaces onto Kählerian spaces

On the theory of the 4-quasiplanar mappings of almost quaternionic spaces

On almost geodesic mappings $π_{2} (e)$ onto Riemannian spaces

$F$ -Планарные преобразования пространств аффинной связности

Conformally geodesic mappings satisfying a certain initial condition

On special almost geodesic mappings of type $π_{1}$ of spaces with affine connection

On tensor fields semiconjugated with torse-forming vector fields

On a classification of almost geodesic mappings of affine connection spaces

Shells of monotone curves

On holomorphically projective mappings from manifolds with equiaffine connection onto Kähler manifolds

On $F_{2}^{ε}$ -planar mappings of (pseudo-) Riemannian manifolds

Equipping distributions for linear distribution

On $f$ -planar mappings of affine-connection spaces with infinite dimension

On scalar and total scalar curvatures of Riemann-Cartan manifolds

The Projectivization of Conformal Models of Fibrations Determined by the Algebra of Quaternions