Publication detail

Differential Geometry of Special Mappings

VANŽUROVÁ, A. STEPANOVA, E. MIKEŠ, J. CHEPURNA, O. CHUDÁ, H. STEPANOV, S. TSYGANOK, I. HADDAD, M. BÁSCÓ, S. BEREZOVSKI, V. JUKL, M. PEŠKA, P. SHANDRA, I. GAVRILCHENKO, M. MOLDOBAEV, D. SOBCHUK, V. SMETANOVÁ, D. JUKLOVA, L. HINTERLEITNER, I. CHODOROVÁ, M. SHIHA, M.

Original Title

Differential Geometry of Special Mappings

English Title

Differential Geometry of Special Mappings

Type

book

Language

en

Original Abstract

The monograph deals with the theory of conformal, geodesic, holomorphically projective, F-planar and others mappings and transformations of manifolds with affine connection, Riemannian, Kahler and Riemann-Finsler manifolds. Concretely, the monograph treats the following: basic concepts of topological spaces, the theory of manifolds with affine connection (particularly, the problem of semigeodesic coordinates), Riemannian and Kahler manifolds (reconstruction of a metric, equidistant spaces, variational problems in Riemannian spaces, SO(3)-structure as a model of statistical manifolds, decomposition of tensors), the theory of differentiable mappings and transformations of manifolds (the problem of metrization of affine connection, harmonic diffeomorphisms), conformal mappings and transformations (especially conformal mappings onto Einstein spaces, conformal transformations of Riemannian manifolds), geodesic mappings (GM; especially geodesic equivalence of a manifold with affine connection to an equiaffine manifold), GM onto Riemannian manifolds, GM between Riemannian manifolds (GM of equidistant spaces, GM of Vn(B) spaces, its field of symmetric linear endomorphisms), GM of special spaces, particularly Einstein, Kahler, pseudosymmetric manifolds and their generalizations, global geodesic mappings and deformations, GM between Riemannian manifolds of different dimensions, global GM, geodesic deformations of hypersurfaces in Riemannian spaces, some applications of GM to general relativity, namely three invariant classes of the Einstein equations and geodesic mappings, F-planar mappings of spaces with affine connection, holomorphically projective mappings (HPM) of Kahler manifolds (fundamental equations of HPM, HPM of special Kahler manifolds, HPM of parabolic Kahler manifolds, almost geodesic , which generalize geodesic mappings, Riemann-Finsler spaces and their geodesic mappings, geodesic mappings of Berwald spaces onto Riemannian spaces.

English abstract

The monograph deals with the theory of conformal, geodesic, holomorphically projective, F-planar and others mappings and transformations of manifolds with affine connection, Riemannian, Kahler and Riemann-Finsler manifolds. Concretely, the monograph treats the following: basic concepts of topological spaces, the theory of manifolds with affine connection (particularly, the problem of semigeodesic coordinates), Riemannian and Kahler manifolds (reconstruction of a metric, equidistant spaces, variational problems in Riemannian spaces, SO(3)-structure as a model of statistical manifolds, decomposition of tensors), the theory of differentiable mappings and transformations of manifolds (the problem of metrization of affine connection, harmonic diffeomorphisms), conformal mappings and transformations (especially conformal mappings onto Einstein spaces, conformal transformations of Riemannian manifolds), geodesic mappings (GM; especially geodesic equivalence of a manifold with affine connection to an equiaffine manifold), GM onto Riemannian manifolds, GM between Riemannian manifolds (GM of equidistant spaces, GM of Vn(B) spaces, its field of symmetric linear endomorphisms), GM of special spaces, particularly Einstein, Kahler, pseudosymmetric manifolds and their generalizations, global geodesic mappings and deformations, GM between Riemannian manifolds of different dimensions, global GM, geodesic deformations of hypersurfaces in Riemannian spaces, some applications of GM to general relativity, namely three invariant classes of the Einstein equations and geodesic mappings, F-planar mappings of spaces with affine connection, holomorphically projective mappings (HPM) of Kahler manifolds (fundamental equations of HPM, HPM of special Kahler manifolds, HPM of parabolic Kahler manifolds, almost geodesic , which generalize geodesic mappings, Riemann-Finsler spaces and their geodesic mappings, geodesic mappings of Berwald spaces onto Riemannian spaces.

Keywords

Riemannian manifolds; Kähler spaces; geodesic mappings; almost geodesic mappings; F-planar mappings; affine connection; covariant derivative

RIV year

2015

Released

20.08.2015

Publisher

Palacký University Olomouc, ID 333149718

Location

Olomouc

ISBN

978-80-244-4671-4

Book

Differential Geometry of Special Mappings

Edition number

1.

Pages from

1

Pages to

566

Pages count

566

BibTex


@book{BUT119700,
  author="Alena {Vanžurová} and Elena {Stepanova} and Josef {Mikeš} and Olena {Chepurna} and Hana {Chudá} and Sergey {Stepanov} and Irina {Tsyganok} and Michael {Haddad} and Sándor {Báscó} and Vladimir {Berezovski} and Marek {Jukl} and Patrik {Peška} and Igor {Shandra} and Michail {Gavrilchenko} and Dzhanybek {Moldobaev} and Vasilij {Sobchuk} and Dana {Smetanová} and Lenka {Juklova} and Irena {Hinterleitner} and Marie {Chodorová} and Mohsen {Shiha}",
  title="Differential Geometry of Special Mappings",
  annote="The monograph deals with the theory of conformal, geodesic, holomorphically projective, F-planar and others mappings and transformations of manifolds with affine connection, Riemannian, Kahler and Riemann-Finsler manifolds. Concretely, the monograph treats the following: basic concepts of topological spaces, the theory of manifolds with affine connection (particularly, the problem of semigeodesic coordinates), Riemannian and Kahler manifolds (reconstruction of a metric, equidistant spaces, variational problems in Riemannian spaces, SO(3)-structure as a model of statistical manifolds, decomposition of tensors), the theory of differentiable mappings and transformations of manifolds (the problem of metrization of affine connection, harmonic diffeomorphisms), conformal mappings and transformations (especially conformal mappings onto Einstein spaces, conformal transformations of Riemannian manifolds), geodesic mappings (GM; especially geodesic equivalence of a manifold with affine connection to an equiaffine manifold), GM onto Riemannian manifolds, GM between Riemannian manifolds (GM of equidistant spaces, GM of Vn(B) spaces, its field of symmetric linear endomorphisms), GM of special spaces, particularly Einstein, Kahler, pseudosymmetric manifolds and their generalizations, global geodesic mappings and deformations, GM between Riemannian manifolds of different dimensions, global GM, geodesic deformations of hypersurfaces in Riemannian spaces, some applications of GM to general relativity, namely three invariant classes of the Einstein equations and geodesic mappings, F-planar mappings of spaces with affine connection, holomorphically projective mappings (HPM) of Kahler manifolds (fundamental equations of HPM, HPM of special Kahler manifolds, HPM of parabolic Kahler manifolds, almost geodesic , which generalize geodesic mappings, Riemann-Finsler spaces and their geodesic mappings, geodesic mappings of Berwald spaces onto Riemannian spaces.",
  address="Palacký University Olomouc, ID 333149718",
  booktitle="Differential Geometry of Special Mappings",
  chapter="119700",
  howpublished="print",
  institution="Palacký University Olomouc, ID 333149718",
  year="2015",
  month="august",
  pages="1--566",
  publisher="Palacký University Olomouc, ID 333149718",
  type="book"
}