%0 Journal Article
%T Hypersurfaces of Projective ¦Â ¨CChanges
%A Masashi Kitayama
%A Toshikazu Tani
%J Memoirs of the Scientific Sections of the Romanian Academy
%D 2011
%I Publishing House of the Romanian Academy
%X In 1984 C. Shibata investigated the theory of a change which is called a ¦Â -change of Finsler metric [10]. On the other hand, in 1985 a systematic study of geometry of hypersurfaces in Finsler spaces was given by M. Matsumoto [6]. In ¡ì 1, according to Shibata [10] we shall prepare the terminology and notations for the sake of argument. In ¡ì 2, we derive a condition for a ¦Â -change to be projective [10]. In ¡ì 3, we find that a totally geodesic hypersurface (n 1)-dimensional F remains to be a totally geodesic hypersurface (n 1)-dimensional F-bar under the projective ¦Â -change. In the last section, we get the main result that Finslerian hypersurfaces given by the projective ¦Â -change are projectively flat on condition the original Finsler space is projectively flat.
%K Finsler space
%K Projective change and ¦Â-change
%K Hypersurface
%K Projective flat
%U http://www.academiaromana-is.ro/Reviste/mem_sc_st_2011/05_MSS_Kitayama.pdf