Skip to main content
SpringerLink
Log in

Curvature and Schur’s Lemma

  • Chapter
An Introduction to Riemann-Finsler Geometry

Part of the book series: Graduate Texts in Mathematics ((GTM,volume 200))

  • 3287 Accesses

Abstract

The curvature 2-forms of the Chern connection are

$$\boxed{\Omega _j^i: = dw_j^i - w_j^k \wedge w_k^i}$$
((3.1.1))

.

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 49.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 64.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 99.99
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. P. L. Antonelli and R. H. Bradbury, Volterra-Hamilton Models in the Ecology and Evolution of Colonial Organisms, World Scientific, 1996.

    Google Scholar 

  2. P. L. Antonelli, R. S. Ingarden, and M. Matsumoto, The Theory of Sprays and Finsler Spaces with Applications in Physics and Biology, FTPH 58, Kluwer Academic Publishers, 1993.

    Google Scholar 

  3. J. Cheeger and D. Ebin, Comparison Theorems in Riemannian Geometry, North Holland/American Elsevier, 1975.

    Google Scholar 

  4. L. del Riego, Tenseurs de Weyl d’un spray de directions, Theses, Université Scientifique et Medicale de Grenoble, 1973.

    Google Scholar 

  5. P. Foulon, Géométrie des équations différentielles du second ordre, Ann. Inst. Henri Poincaré 45(1) (1986), 1–28.

    MathSciNet  MATH  Google Scholar 

  6. M. Matsumoto, Foundations of Finsler Geometry and Special Finsler Spaces, Kaiseisha Press, Japan, 1986.

    MATH  Google Scholar 

  7. S. Numata, On the torsion tensors Rjhk and Phjk of Finsler spaces with a metric ds = (g ij (dx)dx i dx j)1/2 + b i (x)dx i Tensor, N.S. 32 (1978), 27–31

    MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, University of Houston, University Park, Houston, TX, 77204, USA

    D. Bao

  2. Department of Mathematics, University of California at Berkeley, Berkeley, CA, 94720, USA

    S.-S. Chern

  3. Department of Mathematical Sciences, Indiana University-Purdue University Indianapolis, Indianapolis, IN, 46202, USA

    Z. Shen

Authors
  1. D. Bao
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. S.-S. Chern
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Z. Shen
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

Copyright information

© 2000 Springer Science+Business Media New York

About this chapter

Cite this chapter

Bao, D., Chern, SS., Shen, Z. (2000). Curvature and Schur’s Lemma. In: An Introduction to Riemann-Finsler Geometry. Graduate Texts in Mathematics, vol 200. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-1268-3_3

Download citation

  • DOI: https://doi.org/10.1007/978-1-4612-1268-3_3

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4612-7070-6

  • Online ISBN: 978-1-4612-1268-3

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation