Rizza called this differential geometric structure, defined on even-dimensional manifolds, "Struttura di Finsler quasi Hermitiana":[3] his motivation for the introduction of the concept seems to be the aim of comparing two different structures existing on the same manifold.
[4] Later Ichijyō (1988, p. 1) started calling this structure "Rizza structure", and manifolds carrying it "Rizza manifolds".
[1] The content of this paragraph closely follows references (Rizza 1963) and (Ichijyō 1988), borrowing the scheme of notation equally from both sources.
Precisely, given a differentiable manifold M and one of its points x ∈ M Definition 1.
If the condition holds true, then M is a Rizza Manifold.