RANDERS METRICS WITH SPECIAL PRINCIPAL CURVATURES

The algebraic properties of the Riemann curvature operator have been the coral subject of numerous geometric results in differential geometry. The eigenvalues ·1,...,·n¡1 of the Riemann curvature operator are functions defined on TM0 and are important geometric quantities in Riemann-Finsler geometry. Here, significantly considerable forms of a principal curvature are studied. It is proved that every Randers metric with one principal curvature ·(y) = k(x)F2(y) is of isotropic S-curvature. Moreover, a result on Ricci-quadratic Randers metrics is languidly proved: every Randers metric with one quadratic principal curvature is also of isotropic S-curvature.