On conformal transformations of Finsler metrics

J . Math. Kyoto U niv. (JMKYAZ) 16-1 (1976) 25-50 ( g i i ( x , . ) 6 3 ) " , w h ere g u is th e Finsler m e tric t e n s o r . A n d , from th e fact th at O g ii, as w e ll as g u , must b e a Finsler m etric tensor, he showed that 0 falls in to at m ost a point fu n ctio n . W e sh a ll ca ll th is result K n e b e lm a n ' s th e o re m . In th e conform al theory o f th e Finsler m etrics, it seem s th at few good resu lts a r e o b ta in e d . This situation may inherently be due to Knebelman's th eorem . For example, the concept that a space be conformal to a Riemannian space is meaningless, because such a space is nothing but Riemannian. In order that we obtain really Finsler-like results, it m ight be better that w e obey other definitions.