Geodesic
Components and Local Prehomogeneity
Acta mathematica Universitatis Comenianae, Tome 73 (2004) no. 2 
S. al Ghour. Components and Local Prehomogeneity. Acta mathematica Universitatis Comenianae, Tome 73 (2004) no. 2. http://geodesic.mathdoc.fr/item/AMUC_2004_73_2_a5/
@article{AMUC_2004_73_2_a5,
     author = {S. al Ghour},
     title = {Components and {Local} {Prehomogeneity}},
     journal = {Acta mathematica Universitatis Comenianae},
     year = {2004},
     volume = {73},
     number = {2},
     url = {http://geodesic.mathdoc.fr/item/AMUC_2004_73_2_a5/}
}
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Prehomogeneous components are introduced. Then the concept of local prehomogeneity as a generalization of both prehomogeneity and local homogeneity is introduced. As a generalization of local prehomogeneity, the concept of prelocal prehomogeneity is also introduced. Many results concerning these concepts are obtained. Several counter examples regarding the relations obtained in this paper are given. Many open questions are also proposed.