Skip to main content
Top

2024 | OriginalPaper | Chapter

Rotary Mappings of Equidistant Spaces

Activate our intelligent search to find suitable subject content or patents.

search-config
loading …

Abstract

The paper is devoted to study of rotary mappings equations of two-dimensional equidistant (pseudo-) Riemannian spaces. The general solution of these equations is found beyond these spaces under minimal requirements for the differentiability of the studied objects.

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 340 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Jetzt Wissensvorsprung sichern!

Literature
1.
go back to reference Chudá, H., Mikeš, J. and Sochor, M.: Rotary diffeomorphism onto manifolds with affine connection. Geometry, Integrability & Quantization 18, 130–137 (2017)MathSciNetCrossRef Chudá, H., Mikeš, J. and Sochor, M.: Rotary diffeomorphism onto manifolds with affine connection. Geometry, Integrability & Quantization 18, 130–137 (2017)MathSciNetCrossRef
2.
go back to reference Dini, U.: On a problem in the general theory of the geographical representations of a surface on another. Anali di Mat. 3, 269–294 (1869)CrossRef Dini, U.: On a problem in the general theory of the geographical representations of a surface on another. Anali di Mat. 3, 269–294 (1869)CrossRef
3.
go back to reference Hinterleitner, I. and Mikeš, J.: Geodesic mappings of (pseudo-)Riemannian manifolds preserve class of differentiability. Miskolc Math. Notes 14, No. 2, 575–582 (2013)MathSciNetCrossRef Hinterleitner, I. and Mikeš, J.: Geodesic mappings of (pseudo-)Riemannian manifolds preserve class of differentiability. Miskolc Math. Notes 14, No. 2, 575–582 (2013)MathSciNetCrossRef
4.
go back to reference Hinterleitner, I.: Geodesic mappings on compact Riemannian manifolds with conditions on sectional curvature. Publ. Inst. Math. 94, No. 108, 125–130 (2013)MathSciNetCrossRef Hinterleitner, I.: Geodesic mappings on compact Riemannian manifolds with conditions on sectional curvature. Publ. Inst. Math. 94, No. 108, 125–130 (2013)MathSciNetCrossRef
5.
go back to reference Hinterleitner, I. and Mikeš, J.: Geodesic mappings and differentiability of metrics, affine and projective connections. Filomat 29, 1245–1249 (2015)MathSciNetCrossRef Hinterleitner, I. and Mikeš, J.: Geodesic mappings and differentiability of metrics, affine and projective connections. Filomat 29, 1245–1249 (2015)MathSciNetCrossRef
6.
go back to reference Hinterleitner, I. and Mikeš, J.: Fundamental equations of geodesic mappings and their generalizations. J. Math. Sci. 174, 537–554 (2011)CrossRef Hinterleitner, I. and Mikeš, J.: Fundamental equations of geodesic mappings and their generalizations. J. Math. Sci. 174, 537–554 (2011)CrossRef
7.
go back to reference Kuzmina, I. and Mikeš, J.: On pseudoconformal models of fibrations determined by the algebra of antiquaternions and projectivization of them. Ann. Math. Inform. 42, 57–64 (2013)MathSciNet Kuzmina, I. and Mikeš, J.: On pseudoconformal models of fibrations determined by the algebra of antiquaternions and projectivization of them. Ann. Math. Inform. 42, 57–64 (2013)MathSciNet
9.
go back to reference Leiko, S.: Variational problems for rotation functionals, and spin-mappings of pseudo-Riemannian spaces. Sov. Math. 34, No. 10, 9–18 (1990)MathSciNet Leiko, S.: Variational problems for rotation functionals, and spin-mappings of pseudo-Riemannian spaces. Sov. Math. 34, No. 10, 9–18 (1990)MathSciNet
10.
go back to reference Leiko, S.: Extremals of rotation functionals of curves in a pseudo-Riemannian space, and trajectories of spinning particles in gravitational fields. Russian Acad. Sci. Dokl. Math. 46, 84–87 (1993)MathSciNet Leiko, S.: Extremals of rotation functionals of curves in a pseudo-Riemannian space, and trajectories of spinning particles in gravitational fields. Russian Acad. Sci. Dokl. Math. 46, 84–87 (1993)MathSciNet
11.
go back to reference Leiko, S.: Isoperimetric extremals of a turn on surfaces in Euclidean space \(\mathbb{E}^{3}\). Russ. Math. 40, No. 6, 22–29 (1996) Leiko, S.: Isoperimetric extremals of a turn on surfaces in Euclidean space \(\mathbb{E}^{3}\). Russ. Math. 40, No. 6, 22–29 (1996)
12.
go back to reference Leiko, S.: On the conformal, concircular, and spin mappings of gravitational fields. J. Math. Sci. 90, 1941–1944 (1998)MathSciNetCrossRef Leiko, S.: On the conformal, concircular, and spin mappings of gravitational fields. J. Math. Sci. 90, 1941–1944 (1998)MathSciNetCrossRef
13.
go back to reference Leiko, S.: Isoperimetric problems for rotation functionals of the first and second orders in (pseudo) Riemannian manifolds. Russ. Math. 49, 45–51 (2005) Leiko, S.: Isoperimetric problems for rotation functionals of the first and second orders in (pseudo) Riemannian manifolds. Russ. Math. 49, 45–51 (2005)
14.
15.
16.
go back to reference Mikeš, J., Berezovski, V. E., Stepanova, E. and Chudá, H.: Geodesic mappings and their generalizations. J. Math. Sci. 217, No. 5, 607–623 (2016)MathSciNetCrossRef Mikeš, J., Berezovski, V. E., Stepanova, E. and Chudá, H.: Geodesic mappings and their generalizations. J. Math. Sci. 217, No. 5, 607–623 (2016)MathSciNetCrossRef
17.
go back to reference Mikeš, J., Vanžurová, A. and Hinterleitner, I.: Geodesic mappings and some generalizations. Palacky Univ. Press, Olomouc (2009) Mikeš, J., Vanžurová, A. and Hinterleitner, I.: Geodesic mappings and some generalizations. Palacky Univ. Press, Olomouc (2009)
18.
go back to reference Mikeš, J., et al.: Differential geometry of special mappings. Palacky Univ. Press, Olomouc (2015) Mikeš, J., et al.: Differential geometry of special mappings. Palacky Univ. Press, Olomouc (2015)
19.
go back to reference Mikeš, J., et al.: Differential geometry of special mappings. 2th ed. Palacky University Press, Olomouc (2019) Mikeš, J., et al.: Differential geometry of special mappings. 2th ed. Palacky University Press, Olomouc (2019)
20.
go back to reference Mikeš, J., Rýparová, L. and Chudá, H.: On the theory of rotary mappings. Math. Notes 104, No. 4, 617–620 (2018)MathSciNetCrossRef Mikeš, J., Rýparová, L. and Chudá, H.: On the theory of rotary mappings. Math. Notes 104, No. 4, 617–620 (2018)MathSciNetCrossRef
21.
go back to reference Mikeš, J., Guseva, N. I., Peška, P. and Rýparová, L.: Rotary mappings and projections of a sphere. Math. Notes 110, No. 1, 152–155 (2021)MathSciNetCrossRef Mikeš, J., Guseva, N. I., Peška, P. and Rýparová, L.: Rotary mappings and projections of a sphere. Math. Notes 110, No. 1, 152–155 (2021)MathSciNetCrossRef
22.
go back to reference Mikeš, J., Sochor, M. and Stepanova, E.: On the existence of isoperimetric extremals of rotation and the fundamental equations of rotary diffeomorphism. Filomat 29, No. 3, 517–523 (2015)MathSciNetCrossRef Mikeš, J., Sochor, M. and Stepanova, E.: On the existence of isoperimetric extremals of rotation and the fundamental equations of rotary diffeomorphism. Filomat 29, No. 3, 517–523 (2015)MathSciNetCrossRef
23.
go back to reference Najdanović, M. S., Zlatanović, M. and Hinterleitner, I.: Conformal and geodesic mappings of generalized equidistant spaces. Publ. Inst. Math. 98, No. 112, 71–84 (2015)MathSciNetCrossRef Najdanović, M. S., Zlatanović, M. and Hinterleitner, I.: Conformal and geodesic mappings of generalized equidistant spaces. Publ. Inst. Math. 98, No. 112, 71–84 (2015)MathSciNetCrossRef
24.
go back to reference Najdanović, M. S. and Velimirović, L. S.: On the Willmore energy of curves under second order infinitesimal bending. Miskolc Math. Notes 17, No. 2, 979–987 (2016)MathSciNetCrossRef Najdanović, M. S. and Velimirović, L. S.: On the Willmore energy of curves under second order infinitesimal bending. Miskolc Math. Notes 17, No. 2, 979–987 (2016)MathSciNetCrossRef
25.
go back to reference Petrov, A.: Modeling of the paths of test particles in gravitation theory. Gravit. and the Theory of Relativity 4, No. 5, 7–21 (1968) Petrov, A.: Modeling of the paths of test particles in gravitation theory. Gravit. and the Theory of Relativity 4, No. 5, 7–21 (1968)
26.
go back to reference Peška P., Mikeš J., Ryparová L. and Chepurna O.: On general solutions of equidistant vector fields on two-dimensional (pseudo-) Riemannian spaces. Filomat 37, No. 25, 8569–8574 (2023)MathSciNet Peška P., Mikeš J., Ryparová L. and Chepurna O.: On general solutions of equidistant vector fields on two-dimensional (pseudo-) Riemannian spaces. Filomat 37, No. 25, 8569–8574 (2023)MathSciNet
27.
go back to reference Rýparová, L. and Mikeš, J.: Rotary mappings of surfaces of revolution. Math., Inf. Technol. and Appl. Sci., 2017. Univ. of Defence, Brno, 2017, 208–216 (2017) Rýparová, L. and Mikeš, J.: Rotary mappings of surfaces of revolution. Math., Inf. Technol. and Appl. Sci., 2017. Univ. of Defence, Brno, 2017, 208–216 (2017)
28.
go back to reference Stepanov, S., Shandra, I. and Mikeš, J.: Harmonic and projective diffeomorphisms. J. Math. Sci. 207, 658–668 (2015)MathSciNetCrossRef Stepanov, S., Shandra, I. and Mikeš, J.: Harmonic and projective diffeomorphisms. J. Math. Sci. 207, 658–668 (2015)MathSciNetCrossRef
29.
go back to reference Sinyukov N.S.: Geodesic mappings of Riemannian spaces. Nauka, Moscow (1979) Sinyukov N.S.: Geodesic mappings of Riemannian spaces. Nauka, Moscow (1979)
30.
go back to reference Vinnik, A., Leiko, S.: The property of reciprocity of rotary diffeomorphisms of two-dimensional Riemannian spaces. Differ. Geom. Mnogoobr. Figur 29, 13–16 (1998) Vinnik, A., Leiko, S.: The property of reciprocity of rotary diffeomorphisms of two-dimensional Riemannian spaces. Differ. Geom. Mnogoobr. Figur 29, 13–16 (1998)
31.
go back to reference Zlatanović, M., Velimirović, L. and Stanković, M.: Necessary and sufficient conditions for equitorsion geodesic mapping. J. Math. Anal. Appl. 435, 578–592 (2016)MathSciNetCrossRef Zlatanović, M., Velimirović, L. and Stanković, M.: Necessary and sufficient conditions for equitorsion geodesic mapping. J. Math. Anal. Appl. 435, 578–592 (2016)MathSciNetCrossRef
Metadata
Title
Rotary Mappings of Equidistant Spaces
Author
Lenka Vítková
Copyright Year
2024
DOI
https://doi.org/10.1007/978-3-031-50586-7_11

Premium Partner