Gaussian curvature: A growth parameter for biological structures

The aim of the present work is to define a method that will be able to study the shape of a biological body as well as the scheme of its growth through the tracks of the generated material. What we really may analyse is the resulting body in its final form, with an associated structure of fibres that represents the history of the growing process. If we examine a biological surface, we can recognise the set of coordinate curves that suggests, biologically, the way by which the growing process has happened, mathematically, the parametric equations of the resulting surface. We derive that Gaussian curvature is a fundamental shape growth parameter, because it decreases during time when the development process ends normally. Thus, it could be a powerful tool for knowing in advance if the biological growth is anomalous or not.