Skip to main content
Log in

Are the neutrinos an aspect of riemannian geometry?

Представляют ли нейтрино аспект римановой геометрии?

  • Published:
Il Nuovo Cimento A (1965-1970)

Summary

Space-time with a 1-parameter holonomy group and vanishing scalar curvature is interpreted as describing the neutrinos. An algebraic condition in the curvature tensor is obtained which, for perfect holonomy groups, characterizes the 1-parameter group. Physical interest in recurrent and symmetric spaces is emphasized.

Riassunto

Si interpreta come una descrizione dei neutrini lo spazio-tempo con un gruppo di olonomie ad un parametro e curvatura scalare nulla. Si ottiene una condizione algebrica per il tensore di curvatura che, per gruppi di olonomie perfetti, caratterizza il gruppo ad un parametro. Si mette in evidenza l’interesse fisico per gli spazi ricorrenti e simmetrici.

Реэюме

Рассматривается, что пространство и время в случае 1-параме-трической голономной группы и обрашаюшейся в нуль скалярной кривиэны описывают нейтрино. Получается алгебраическое условие на тенэор кривиэны, которое для идеальных голономных групп характериэует 1-параметрическую группу. Отмечается фиэический интерес к рекуррентным и симметричьым пространствам.

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

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. J. N. Goldberg andR. P. Kerr:Journ. Math. Phys.,10, 327 (1969).

    Article  MathSciNet  Google Scholar 

  2. V. Hlavaty:Rend. Circ. Mat. Palermo,9, 57 (1960).

    Google Scholar 

  3. H. Minkowski:Math. Ann.,68, 472 (1910).

    Article  MATH  MathSciNet  Google Scholar 

  4. A. G. Walker:Proc. London Math. Soc.,52, 36 (1950).

    Article  MathSciNet  Google Scholar 

  5. A bivector field of this type also occurs in:B. Bertotti:Phys. Rev.,116, 1331 (1959);H. Stephani:Commun. Math. Phys.,5, 337 (1967).

    Article  MATH  MathSciNet  ADS  Google Scholar 

  6. Einstein once suggested (Sitz. Preuss. Akad. Wiss., 349 (1919)) the tensorP ab as a possible substitute forS ab in his field equations of gravitation.

  7. G. Y. Rainich:Trans. Am. Math. Soc.,27, 106 (1925).

    Article  MATH  MathSciNet  Google Scholar 

  8. C. W. Misner andA. Wheeler:Ann. of Phys.,2, 525 (1957).

    Article  MATH  MathSciNet  ADS  Google Scholar 

  9. A. Lichnérowicz:Compt. Rend.,246, 893 (1958).

    MATH  Google Scholar 

  10. R. Peneny:Journ. Math. Phys.,6, 1309 (1965).

    Article  MATH  ADS  Google Scholar 

  11. V. Hlavaty:Rend. Circ. Mat. Palermo,9, 125 (1960).

    Article  MATH  MathSciNet  Google Scholar 

  12. H. S. Ruse:Proc. London Math. Soc.,53, 212 (1951).

    Article  MATH  MathSciNet  Google Scholar 

  13. J. A. Schouten:Ricci-Calculus, II ed. (Berlin, 1954), p. 421.

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Öktem, F. Are the neutrinos an aspect of riemannian geometry?. Nuov Cim A 1, 38–48 (1971). https://doi.org/10.1007/BF02722609

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02722609

Navigation