Beiträge zur Algebra und Geometrie Contributions to Algebra and Geometry Vol. 47, No. 1, pp. 289304 (2006) 

Submanifolds in the variety of planar normal sectionsWalter N. Dal Lago, Alicia N. García and Cristián U. SánchezFa. M. A. F. Universidad Nacional de Córdoba, CIEMCONICET, Ciudad Universitaria, 5000 Córdoba, Argentina, email: dallago@mate.uncor.edu email: agarcia@mate.uncor.edu email: csanchez@mate.uncor.eduAbstract: The present paper continues the study of the nature of the variety $X\left[M\right]$ of directions of pointwise planar normal sections for the manifold $M$ of complete flags of a compact simple Lie group $G_{u}$. The main results concern submanifolds embedded in $RP^{m1}$ ($m=\dim M$) which are subsets of $X\left[ M\right]$. One of them is an open set in the natural topology of $X\left[M\right]$ whose dimension is related to that of $M$ and the rank of the Lie group $G_{u}$. Others are projective subspaces of ``minimal'' dimension contained in $X\left[M\right]$ for the groups $G_{u}=SU(n+1)$. Classification (MSC2000): 53C30, 53C42, 32V30 Full text of the article:
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