Abstract
It is known that the geometric methods are used in most fields in natural sciences. Kinematics on curves and surfaces as one of these methods is an essential tool for investigating the growth of some biological objects. In this study, the time‐dependent and quaternionic models of accretive growth are considered. For this, first, it is defined as a growth velocity in the direction of the Darboux vector at every point on a spatial non‐null curve in three‐dimensional Lorentz–Minkowski spacetime. Second, accretive surface growth is presented through quaternions. With the help of the quaternionic form of the growth model, we reach that a point (cell tract) on the accretive surface makes a homothetic motion. Also, several examples and visualizations are given to support the theory.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
