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Journal of Lie Theory 23 (2013), No. 4, 1129--1160
Copyright Heldermann Verlag 2013

Castling Transformations of Projective Structures

Hironao Kato
Advanced Mathematical Institute, Osaka City University, 3-3-138 Sugimoto, Sumiyoshi-ku, Osaka 558-8585, Japan
and: Dept. of Mathematics, King's College, Strand, London WC2R 2LS, England

We construct an infinite sequence of projectively flat manifolds by using castling transformations of prehomogeneous vector spaces. We also give a classification of manifolds equipped with a flat projective structure obtained by a finite number of castling transformations, and describe these flat projective structures by atlases.

Keywords: Projective structure, Grassmannian structure, prehomogeneous vector space.

MSC: 53B10, 11S90; 53C10

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