Skip to main content
SpringerLink
Log in

Geodesic Mappings and Einstein Spaces

  • Conference paper
  • First Online:
Book cover Geometric Methods in Physics

Part of the book series: Trends in Mathematics ((TM))

Abstract

In this paper we study fundamental properties of geodesic mappings with respect to the smoothness class of metrics. We show that geodesic mappings preserve the smoothness class of metrics. We study geodesic mappings of Einstein spaces.

Mathematics Subject Classification (2010). 53C21; 53C25; 53B21; 53B30.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 129.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 169.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. L.P. Eisenhart, Non-Riemannian Geometry. Princeton Univ. Press. 1926. Amer. Math. Soc. Colloquium Publications 8 (2000).

    Google Scholar 

  2. J. Mikeš, Geodesic mappings of affine-connected and Riemannian spaces. J. Math. Sci., New York 78 (1996) 311–333.

    Google Scholar 

  3. J. Mikeš, A. Vanžurová, I. Hinterleitner, Geodesic mappings and some generalizations. Palacky University Press, 2009.

    Google Scholar 

  4. Zh. Radulovich, J. Mikeš, M.L. Gavril’chenko, Geodesic mappings and deformations of Riemannian spaces. (Russian) Podgorica: CID. Odessa: OGU, 1997.

    Google Scholar 

  5. N.S. Sinyukov, Geodesic mappings of Riemannian spaces. M., Nauka, 1979.

    Google Scholar 

  6. L.D. Kudrjavcev, Kurs matematicheskogo analiza. Moscow, Vyssh. skola, 1981.

    Google Scholar 

  7. J. Mikeš, Holomorphically projective mappings and their generalizations. J. Math. Sci., New York 89 (1998) 1334–1353.

    Google Scholar 

  8. A.Z. Petrov, New methods in the general theory of relativity. M., Nauka, 1966.

    Google Scholar 

  9. J. Mikeš, Geodesic and holomorphicaly mappings of special Riemannian spaces. PhD thesis, Odessa, 1979.

    Google Scholar 

  10. J. Mikeš, Geodesic mappings of Einstein spaces. Math. Notes 28 (1981) 922–923; transl. from Mat. Zametki 28 (1980) 935–938.

    Google Scholar 

  11. J. Mikeš, V.A. Kiosak, On geodesic maps of four dimensional Einstein spaces. Odessk. Univ. Moscow: Archives at VINITI, 9.4.82, No. 1678–82, (1982).

    Google Scholar 

  12. S. Formella, J. Mikeš, Geodesic mappings of Einstein spaces. Szczecińske rocz. naukove, Ann. Sci. Stetinenses. 9 I. (1994) 31–40.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Dept. of Math., Brno University of Technology, Žižkova 17, CZ-60200, Brno, Czech Republic

    Irena Hinterleitner

  2. Dept. of Algebra and Geometry, Palacky University, 17. listopadu 12, CZ-77146, Olomouc, Czech Republic

    Josef Mikeš

Authors
  1. Irena Hinterleitner
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Josef Mikeš
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Irena Hinterleitner .

Editor information

Editors and Affiliations

  1. Departamento de Física, CINVESTAV, Mexico City, Distrito Federal, Mexico

    Piotr Kielanowski

  2. Dept. of Mathematics and Statistics, Concordia University, Montreal, Québec, Canada

    S. Twareque Ali

  3. Institute of Mathematics, University of Bialystok, Bialystok, Poland

    Anatol Odzijewicz

  4. Mathematics Research Unit, FSTC, University of Luxembourg, Luxembourg-Kirchberg, Luxembourg

    Martin Schlichenmaier

  5. School of Mathematics, University of Manchester, Manchester, United Kingdom

    Theodore Voronov

Rights and permissions

Reprints and permissions

Copyright information

© 2013 Springer Basel

About this paper

Cite this paper

Hinterleitner, I., Mikeš, J. (2013). Geodesic Mappings and Einstein Spaces. In: Kielanowski, P., Ali, S., Odzijewicz, A., Schlichenmaier, M., Voronov, T. (eds) Geometric Methods in Physics. Trends in Mathematics. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-0448-6_28

Download citation

Publish with us

Policies and ethics

Search

Navigation