Dually Flat Fourth Root Metric
作者: 徐 兵 ：宁波大学数学系;
Abstract: In this paper, we mainly study three kinds of Finsler metrics which have the square root, and get some differential equations when they are dually flat. Furthermore, we discuss the relationship between the three kinds of Finsler metrics.
文章引用: 徐 兵 (2013) 对偶平坦的四次根式度量。 理论数学， 3， 195-200. doi: 10.12677/PM.2013.33029
 S.-I. Amari, H. Nagaoka. Method of Information Geometry. AMS Translation of Math, Oxford University Press, 2000, Monographs, 191.
 Z. Shen. Riemann-Finsler geometry with applications to information geometry. Chin. Ann. Math, 2006, 27B(1): 73-94.
 Z. Shen, X. Y. Cheng and Y. S. Zhou. On a class of locally dually flat Finsler metrics. Journal of Hokkaido University of Education (Section II A), 1995, 46(1): 1-10.
 L. Astola, L. Florack. Finsler geometry on higher order tensor fields and applications to high angular resolution diffusion imaging, scale space and variational methods in computer vision. Lecture Notes in Computer Science, 2009, 5567: 224-234.
 D. G. Pavlow. Space-time structure, collected papers. TETRU, 2006: 352 p.
 A. Tayebi, B. Najafi. On m-th root Finsler metrics. Journal of Geometry and Physics, 2011, 61(8): 1479-1484.
 B. Li, Z. Shen. Protectively flat fourth root Finsler metrics. Canadian Mathematical Bulletin, 2012, 55(1): 138-145.
 Z. Shen. On protectively flat -metrics. Canadian Mathematical Bulletin, 2009, 52(1): 132-144.