H. A. Wilbrink [Geom. Dedicata 12 (1982)] considered a class of Minkowski planes whose restrictions, called residual planes, are nearaffine planes. Our study goes in the opposite direction: what conditions on a nearaffine plane are necessary and sufficient to get an extension which is a hyperbola structure.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-ba55-1-8, author = {Kinga Cudna-Salmanowicz and Jan Jak\'obowski}, title = {Extending Nearaffine Planes to Hyperbola Structures}, journal = {Bulletin of the Polish Academy of Sciences. Mathematics}, volume = {55}, year = {2007}, pages = {71-80}, zbl = {1116.51001}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ba55-1-8} }
Kinga Cudna-Salmanowicz; Jan Jakóbowski. Extending Nearaffine Planes to Hyperbola Structures. Bulletin of the Polish Academy of Sciences. Mathematics, Tome 55 (2007) pp. 71-80. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ba55-1-8/