Editing Hilbert's fourth problem (section)

==Unsolved problems==
# Hilbert's fourth problem  for non-symmetric Finsler metric has not yet been solved.
# The description of the metric on <math>RP^{n}</math> for which ''k''-planes minimize the ''k''-area has not been given (Busemann).<ref name="Papadopoulos2004">{{cite book
| last1=Papadopoulos | first1=Athanase
| chapter-url=https://hal.archives-ouvertes.fr/hal-00916933/document
| chapter=Hilbert's fourth problem
| pages=391–431
| title=Handbook of Hilbert geometry
| editor-last1=Papadopoulos | editor-first1=Athanase
| editor-last2=Troyanov | editor-first2=Marc
| publisher=European Mathematical Society
| series=IRMA Lectures in Mathematics and Theoretical Physics
| volume=22
| date=2014
| doi=10.4171/147-1/15| isbn=978-3-03719-147-7
}}</ref>