Skip to main content
SpringerLink
Log in

The extra dimensions of the eleven-dimensional simple supergravity are ricci-flat if they are compact

  • Published:
Lettere al Nuovo Cimento (1971-1985)

Summary

By using the de Rham-Yano-Bochner lemma on harmonic tensor fields in a compact orientable manifold, we show that the extra dimensions in eleven-dimensional simple supergravity will he Ricci-flat if they are compact.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. E. Cremmer, B. Julia andJ. Scherk:Phys. Lett. B,76, 409 (1978).

    Article  ADS  Google Scholar 

  2. P. G. O. Freund andM. A. Rubin:Phys. Lett. B,97, 233 (1980).

    Article  MathSciNet  ADS  Google Scholar 

  3. F. Englert:Phys. Lett. B,119, 339 (1982).

    Article  ADS  Google Scholar 

  4. M. A. Awada, M. J. Duff andC. N. Pope:Phys. Rev. Lett.,50, 294 (1983);M. J. Duff,B. E. W. Nillson andC. N. Pope:Phys. Rev. Lett.,50, 2043 (1983).

    Article  MathSciNet  ADS  Google Scholar 

  5. G. de Rham:Ann. Univ. Grenoble,23, 55 (1947).

    Google Scholar 

  6. K. Yano:Ann. Math.,55, 328 (1952).

    Article  ADS  Google Scholar 

  7. S. Bachner:Bull. Am. Math. Soc., 334 (1937).

Download references

Author information

Authors and Affiliations

  1. Department of Physics, National Central University, Ghungli, 320, Taiwan, Republic of China

    Ming-Quey Chen, De-Ching Chern, Rue-Ron Hsu & Wai Bong Yeung

Authors
  1. Ming-Quey Chen
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. De-Ching Chern
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Rue-Ron Hsu
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Wai Bong Yeung
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Partially supported by the National Science Counil of the Republic of China under contract number NSC-73-0208-M008-04.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Chen, MQ., Chern, DC., Hsu, RR. et al. The extra dimensions of the eleven-dimensional simple supergravity are ricci-flat if they are compact. Lett. Nuovo Cimento 41, 170–172 (1984). https://doi.org/10.1007/BF02747268

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02747268

PACS

Search

Navigation