  We study two types of isotropic planes: weakly isotropic and strongly
isotropic planes. We prove that a Riemannian manifold of indefinite metric is
conformally flat if and only if its curvature tensor vanishes on all the
strongly isotropic planes. We specialize the plane axiom for Riemannian
manifolds of indefinite metrics. We show that manifolds satisfying plane axiom
of weakly (strongly) isotropic planes are of constant sectional curvature
(conformaly flat). Further we study analogous problems on almost Hermitian
manifolds of indefinite metrics.
