Abstract
We study the setX[M] of planar normal sections on the natural imbedding of a flag manifoldM. We characterizeX[M] and show that it is a real algebraic submanifold of ℝP n (n=dimM). From results of Chen and Ferus, it may be concluded thatX[M] measures how farM is from a symmetricR-space. We compute the Euler characteristic ofX[M] and its complexificationX c [M]. Our main result shows, in particular, thatx(X[M]) andx(X c [M]) depend only on dimM and not on the nature ofM itself.
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Dal Lago, W., García, A. & Sánchez, C. Planar normal sections on the natural imbedding of a flag manifold. Geom Dedicata 53, 223–235 (1994). https://doi.org/10.1007/BF01264024
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DOI: https://doi.org/10.1007/BF01264024