On the variety of planar normal sections

ALICIA N. GARCÍA; WALTER DAL LAGO; CRISTIÁN U. SÁNCHEZ

REVISTA DE LA UNIóN MATEMáTICA ARGENTINA

Unión Matemática Argentina

Lugar: Bahía Blanca; Año: 2006 vol. 47 p. 115 - 123

0041-6932

. In the present paper we present a survey of results concerning the variety X [M] of planar normal sections associated to a natural embedding of a real flag manifold Mm. The results included are those that, we feel, better describe the nature of this algebraic variety of RPm. In particular we present results concerning its Euler characteristic showing that it depends only on dimM and not on the nature of M itself. Furthermore, when M is the manifold of complete flags of a compact simple Lie group, we present what is, in some sense, its dimension and a large class of submanifolds of RPm contained in X [M].