Narasimhamurthy, S. K.; Aveesh, S. T.; Kumar, P.; Nagaraja, H. G. Special Finsler spaces admitting metric like tensor field. (English) Zbl 1173.53036 Int. J. Math. Anal., Ruse 3, No. 1-4, 15-21 (2009). This paper studies special Finsler spaces such as \(C\)-reducible, semi-\(C\)-reducible, quasi-\(C\)-reducible with the \(T\)-condition which are admitting a tensor field \(X_{hk}=h_{hk}+X_{00}l_hl_k\) that satisfies the condition \(C^h_{ij} X_{hk}=C_{ijk}\). But any concrete example of such tensor field \(X_{hk}\) is not found up to the present. There is a wrong situation.The authors use the notions of semi-\(C\)-reducible [M. Matsumoto and S. Numata, Tensor, New Ser. 34, 218–222 (1980; Zbl 0435.53023)] and \(T\)-condition [H. Rund, The differential geometry of Finsler spaces. Heidelberg: Springer-Verlag (1959; Zbl 0087.36604)] without dimension restriction. It is also remarked that the \(T\)-condition was first defined in [M. Matsumoto, Foundations of Finsler geometry and special Finsler spaces. Shiga-Ken 520, Japan: Kaiseisha Press (1986; Zbl 0594.53001), p.189] and it should be noted that \(l_ml^m=l\). Reviewer: Hideo Shimada (Sapporo) MSC: 53C60 Global differential geometry of Finsler spaces and generalizations (areal metrics) Keywords:Finsler space; C-reducible; semi-C-reducible; C2-like; quasi- C-reducible; S3-like; P-reducible; T-condition Citations:Zbl 0435.53023; Zbl 0087.36604; Zbl 0594.53001 PDFBibTeX XMLCite \textit{S. K. Narasimhamurthy} et al., Int. J. Math. Anal., Ruse 3, No. 1--4, 15--21 (2009; Zbl 1173.53036) Full Text: Link