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Constant Flag Curvature Spaces and Akbar-Zadeh’s Theorem

  • D. Bao
  • S.-S. Chern
  • Z. Shen
Part of the Graduate Texts in Mathematics book series (GTM, volume 200)

Abstract

In §3.9, we encountered the flag curvature. As the name suggests, this quantity (denoted K) involves a location x ϵ M, a flagpole ℓ:= with y ϵ T x M, and a transverse edge V ϵ T x M. The precise formula is quite elegantly given by (3.9.3):
$$K(\ell ,V): = \frac{{{V^i}({\ell ^j}{R_{jikl}}{\ell ^l}){V^k}}}{{g(\ell ,\ell )g(V,V) - {{[g(\ell ,V)]}^2}}} = \frac{{{V^i}{R_{ik}}{V^k}}}{{g(V,V) - {{[g(\ell ,V)]}^2}}}$$
.

Keywords

Integral Curve Finsler Space Finsler Manifold Chern Connection Finsler Structure 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media New York 2000

Authors and Affiliations

  • D. Bao
    • 1
  • S.-S. Chern
    • 2
  • Z. Shen
    • 3
  1. 1.Department of MathematicsUniversity of HoustonUniversity Park, HoustonUSA
  2. 2.Department of MathematicsUniversity of California at BerkeleyBerkeleyUSA
  3. 3.Department of Mathematical SciencesIndiana University-Purdue University IndianapolisIndianapolisUSA

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