@article{oai:niigata-u.repo.nii.ac.jp:00002183, author = {Innami, Nobuhiro}, issue = {1}, journal = {Nihonkai Mathematical Journal, Nihonkai Mathematical Journal}, month = {}, note = {In the present paper circles and ellipses will be characterized by some properties of billiard ball trajectories. Those properties will be discussed in connection with the characterization of flat metrics on tori by some families of geodesics and tori of revolution. The main method is the geometry of geodesics due to H. Busemann which was reconstructed in the configuration space by V. Bangert. In particular, the theory of parallels plays an important role in the present paper.}, pages = {73--120}, title = {Geometry of geodesics for convex billiards and circular billiards}, volume = {13}, year = {2002} }