Normality of the Hyper-Surfaces of Almost Hermite Manifods

Abstract

An even-dimensional differentiable manifold V_2m on which there are defined a tensor field F of the type (1,1) and a metric-tensor field g, satisfying for arbitrary vector fields λ, μ, v, . . . ∈ V_2m,
F²=-I_2m, (1.1a)
'F(λ,μ)=g(Fλ,μ)=-'F(μ,μ), (1.1b)
is called an almost Hermite manifold with the almost Hermite structure {F,g} (Helgason, 1960; Yano, 1965; Mishra, 1984, p. 67).