The equations of the de Broglie wave field (field equations) [J. Kulhanek, Nuovo Cimento Supp. 4, 172 (1966)] under special conditions require a very particular geometry together with a specific interpretation of the curvature scalar. The purpose of the present paper is to show that the same condition turns the conservation law (which is a consequence of the field equations) into an identity and that the Rainich [Nature 115, 498 (1925)] decomposition of Riemann's curvature tensor gives only one component.