On s-Wagner spaces of W-scalar curvature (Q1824870)

\textit{M. Hashiguchi} and \textit{T. Varga} [Stud. Sci. Math. Hung. 14, 11-14 (1979; Zbl 0424.53014)] studied Wagner spaces of W-scalar curvature and showed a result on s-Wagner spaces of W-scalar curvature similar to the one proved independently by \textit{S. Numata} [J. Korean Math. Soc. 12, 97- 100 (1975; Zbl 0314.53017)] and \textit{T. Varga} [Publ. Math. 25, 213-223 (1978; Zbl 0394.53013)] for Berwald space of scalar curvature. In the present paper, we give another proof of the above theorem in the form of the following statement. Theorem. An n (\(\geq 3)\)-dimensional s- Wagner space of non-zero W-scalar curvature is a Riemannian space. We preface the proof of this theorem by obtaining expressions for (v) h- torsion tensor and h-curvature tensor of an s-Wagner space of W-scalar curvature K. Moreover, we observe that these expressions are the formulas for a Riemannian space conformal to a Riemannian space of constant curvature.