2 citations · 2 across the 4 of their papers we have counts for
4 papers
Projectively flat and affinely flat parabolic subgroups of special linear groups
Hironao Kato
A special linear Lie group over the real number field and the quarternion field admits a projectivley flat affine connection. We show that parabolic subgroups are autoparallel subm…
Left invariant flat projective structures on Lie groups and prehomogeneous vector spaces
Hironao Kato
We show the correspondence between left invariant flat projective structures on Lie groups and certain prehomogeneous vector spaces. Moreover by using the classification theory of…
Low dimensional Lie groups admitting left invariant flat projective or affine structures
Hironao Kato
We prove that any real Lie group of dimension \leq 5 admits a left invariant flat projective structure. We also prove that a real Lie group L of dimension \leq 5 admits a left inva…
Castling transformations of projective structures
Hironao Kato
We construct an infinite sequence of projectively flat manifolds by using castling transformations of prehomogeneous vector spaces. We also give a classification of manifolds equip…