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)


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):
$$K(\ell ,V): = \frac{{{V^i}({\ell ^j}{R_{jikl}}{\ell ^l}){V^k}}}{{g(\ell ,\ell )g(V,V) - {{[g(\ell ,V)]}^2}}} = \frac{{{V^i}{R_{ik}}{V^k}}}{{g(V,V) - {{[g(\ell ,V)]}^2}}}$$


Manifold Assure Verse sinO 


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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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