Skip to main content

Gaussian Differential Geometry and Differential Geodesy

  • Conference paper
V Hotine-Marussi Symposium on Mathematical Geodesy

Part of the book series: International Association of Geodesy Symposia ((IAG SYMPOSIA,volume 127))

  • 256 Accesses

Abstract

This paper presents an appreciation of the work of Marussi and Hotine, and gives a survey of my investigations of Gaussian differential geometry which are required in formulating the generalized Marussi-Hotine approach to differential geodesy. It is not intended to be either a comprehensive survey, or a status report, on the beautiful contributions of other authors in different approaches to differential geodesy.

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

Access this chapter

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 169.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 219.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 219.99
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.

Similar content being viewed by others

References

  1. Gauss, C. F. (1825). Allgemeine Auflösung der Aufgabe: Die Theile einer gegebnen Fläche auf einer andern gegebnen Fläche so abzubilden, dass die Abbildung der Abgebildeteen in den kleinsten Theilen ähnlich wird, Astronomischen Nachrichten. 3: 1–30

    Article  Google Scholar 

  2. Gauss, C. F. (1828). Disquisitiones generales circa superficies curves. Commentationes societatis regiae scientiarum Göttingensis, Commentationes classis mathematicae 6: 99–146

    Google Scholar 

  3. Hotine, M. (1970). Mathematical Geodesy, U. S. Department of Commerce, Washington, D. C.

    Google Scholar 

  4. Hotine, M. (1991). Differential Geodesy, Zund J. D., Nolton J., Chovitz B. H., Whitten C. A. (eds) Springer-Verlag, Berlin.

    Google Scholar 

  5. Marussi, A. (1949). Fondements de géométrie différentielle absolue du champ potentiel terrestre. Bulletin Géodésique, 14, pp. 411–439.

    Article  Google Scholar 

  6. Marussi, A (1985). Intrinsic Geodesy. (translated by W. I. Reilly), Springer-Verlag, Berlin.

    Book  Google Scholar 

  7. Marussi, A. (1988). Intrinsic Geodesy, (a revised and edited version of his 1952 lectures prepared by J. D. Zund), Report Number 390, Department of Geodetic Science and Surveying, The Ohio State University, Columbus.

    Google Scholar 

  8. McConnell, J. A. (1931). Applications of the absolute fferential calculus. Blackie & Son, Limited, London (reprinted as Applications of tensor analysis,by Dover Publications, Inc., New York, (1957)).

    Google Scholar 

  9. Ricci, G. (1898). Lezioni sulla teoria della superficie. Fratelli Drucker - Editore, Verona - Padova.

    Google Scholar 

  10. Zund, J. D. (1988). Tensorial methods in classical differential geometry I: basic principles. Tensor N. S. 47, pp. 73–82.

    Google Scholar 

  11. Zund, J. D. (1988). Tensorial methods in classical differential geometry II: basic surface tensors. Tensor N. S. 47, pp. 83–92.

    Google Scholar 

  12. Zund, J. D. (1990). An essay on the mathematical foundations of the Marussi-Hotine approach to geodesy. Bolletino di Geodesia e Scienze Affini XLIX, pp. 133–179.

    Google Scholar 

  13. Zund, J. D. (1991). The work of Antonio Marussi in theoretical geodesy. Proceedings of the Geodetic Day in honor of Antonio Marussi. Accademia Nazionale dei Lincei, Rome.

    Google Scholar 

  14. Zund, J. D. (1994). Foundations of differential geodesy. Springer-Verlag, Berlin.

    Book  Google Scholar 

  15. Zund, J. D. (1996). An essay on the foundations of Gaussian differential geometry I: completeness questions. Bolletino di Geodesia e Scienze Affini LV, pp. 377–384.

    Google Scholar 

  16. Zund, J. D. (1997). An essay on the foundations of Gaussian differential geometry II: imbedding questions. Bolletino di Geodesia e Scienze Affini LVI, pp. 407–424.

    Google Scholar 

  17. Zund, J. D. (1998). An essay on the foundations of Gaussian differential geometry III: sphere geometry. Bolletino di Geodesia e Scienze Affini LVII, pp. 309–321.

    Google Scholar 

  18. Zund, J. D.(199). An essay on the foundations of Gaussian differential geometry IV: the parametrization problem. Bolletino di Geodesia e Scienze Affini LVIII, pp. 325–352.

    Google Scholar 

  19. Zund, J. D. (2000). An essay on the foundations of Gaussian differential geometry V: operator methods. Bolletino di Geodesia e Scienze Affini LIX, pp. 351–368.

    Google Scholar 

  20. Zund, J. D. (2001). An essay on the foundations of Gaussian differential geometry VI: the reciprocal Gauss operator. Bolletino di Geodesia e Scienze Affini LX, pp. 191–212.

    Google Scholar 

  21. Zund, J. D. (2003). An essay on the foundations of Gaussian differential geometry VII: the parametrization problem revisited, Bolletino di Geodesia e Scienze Affini, LXII, 63–76.

    Google Scholar 

  22. Zund, J. D. (2003). An essay on the foundations of Gaussian differential geometry VIII: the leg integrability conditions, Bolletino di Geodesia e Scienze Affini,LXII, in press.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2004 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Zund, J.D. (2004). Gaussian Differential Geometry and Differential Geodesy. In: Sansò, F. (eds) V Hotine-Marussi Symposium on Mathematical Geodesy. International Association of Geodesy Symposia, vol 127. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-10735-5_2

Download citation

  • DOI: https://doi.org/10.1007/978-3-662-10735-5_2

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-06028-1

  • Online ISBN: 978-3-662-10735-5

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics