An ellipse in R2 can be defined as the locus of points for which the sum of the Euclidean distances from the two foci is constant. In this paper we will look at the sets that are obtained by considering in the above definition distances induced by arbitrary norms.
@article{urn:eudml:doc:41842, title = {Metric ellipses in Minkowski planes.}, journal = {Extracta Mathematicae}, volume = {20}, year = {2005}, pages = {273-280}, zbl = {1119.52002}, mrnumber = {MR2243343}, language = {en}, url = {http://dml.mathdoc.fr/item/urn:eudml:doc:41842} }
Senlin, Wu; Donghai, Ji; Alonso, Javier. Metric ellipses in Minkowski planes.. Extracta Mathematicae, Tome 20 (2005) pp. 273-280. http://gdmltest.u-ga.fr/item/urn:eudml:doc:41842/