caa a22 4500 605462062 CHVBK 20210128100246.0 cr unu---uuuuu 210128e20150501xx s 000 0 eng 10.1007/s10114-015-2584-6 doi (NATIONALLICENCE)springer-10.1007/s10114-015-2584-6 On conformally flat ( α , β )-metrics with special curvature properties [Elektronische Daten] [Min Yuan, Xin Cheng] In this paper, we study a significant non-Riemannian quantity Ξ-curvature, which is defined by S-curvature. Firstly, we obtain the formula of Ξ-curvature for (α, β)-metrics. Based on it, we show that the Ξ-curvature vanishes for a class of (α, β)-metrics. In the end, we get the relation of Ξ-curvature for conformally related Finsler metrics, and classify conformally flat (α, β)-metrics with almost vanishing Ξ-curvature. Institute of Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Chinese Mathematical Society and Springer-Verlag Berlin Heidelberg, 2015 ( α , β )-metrics nationallicence conformally flat nationallicence Ξ-curvature nationallicence Yuan Min Department of Mathematical Sciences, Indiana University Purdue University Indianapolis, 402 N Blackford Street, 46202, Indianapolis, IN, USA aut Cheng Xin School of Mathematics and Statistics, Chongqing University of Technology, 400054, Chongqing, P. R. China aut Acta Mathematica Sinica, English Series Institute of Mathematics, Chinese Academy of Sciences and Chinese Mathematical Society 31/5(2015-05-01), 879-892 1439-8516 31:5<879 2015 31 10114 https://doi.org/10.1007/s10114-015-2584-6 text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s10114-015-2584-6 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Yuan Min Department of Mathematical Sciences, Indiana University Purdue University Indianapolis, 402 N Blackford Street, 46202, Indianapolis, IN, USA aut NATIONALLICENCE 700 1- Cheng Xin School of Mathematics and Statistics, Chongqing University of Technology, 400054, Chongqing, P. R. China aut NATIONALLICENCE 773 0- Acta Mathematica Sinica, English Series Institute of Mathematics, Chinese Academy of Sciences and Chinese Mathematical Society 31/5(2015-05-01), 879-892 1439-8516 31:5<879 2015 31 10114