Acta Mathematica Sinica, English Series

, Volume 26, Issue 8, pp 1457–1462 | Cite as

The signature of generalized flag manifolds and applications



Let G be a linear algebraic group over ℂ and P be a parabolic subgroup. We determine the signatures of the flag manifold G/P. As an application, we prove that the nonsingular hypersurfaces of degree 2 in ℂP n are prime if n satisfies certain conditions.


Signature flag manifold prime manifold 

MR(2000) Subject Classification

57T15 57R19 


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Copyright information

© Institute of Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Chinese Mathematical Society and Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  1. 1.Department of MathematicsTongji UniversityShanghaiP. R. China
  2. 2.Institute of Mathematics, Academy of Mathematics and System ScienceChinese Academy of SciencesBeijingP. R. China

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