
In this paper an extension of the 2 2 -number ( # 2 ( M ) ) ({\# _2}(M)) of a symmetric space is given for k k -symmetric spaces. The new invariant is computed for flag manifolds which are not symmetric. It turns out to be equal to the Euler-Poincaré characteristic.
\(k\)-number, Differential geometry of homogeneous manifolds, \(k\)-symmetric Riemannian spaces, Betti numbers, Euler characteristic, Morse theory, flag manifold, Differential geometry of symmetric spaces
\(k\)-number, Differential geometry of homogeneous manifolds, \(k\)-symmetric Riemannian spaces, Betti numbers, Euler characteristic, Morse theory, flag manifold, Differential geometry of symmetric spaces
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