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Pseudo null growth model and its classifications based on generalized vortex filament equation.

Jinhua Qian1, Yao Guo1, Young Ho Kim2

  • 1Department of Mathematics, Northeastern University, Shenyang 110819, People's Republic of China.

Heliyon
|November 25, 2022
PubMed
Summary

This study introduces a pseudo null growth model in Minkowski 3-space, evolving pseudo null curves to define geometric properties. Generalized Hasimoto surfaces are explored using the vortex filament equation, revealing their conditions and structures.

Keywords:
Hasimoto surfaceMinkowski spacePseudo null growth surfaceStructure function

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Area of Science:

  • Differential Geometry
  • Mathematical Physics

Background:

  • The study of curve evolution and surface generation is fundamental in differential geometry.
  • The vortex filament equation has been a key tool in understanding the dynamics of curves and surfaces.

Purpose of the Study:

  • To develop a pseudo null growth model for curves in Minkowski 3-space.
  • To propose and investigate generalized Hasimoto surfaces derived from the vortex filament equation.
  • To analyze the geometric structures and conditions of these novel surfaces.

Main Methods:

  • Evolving pseudo null curves by considering their direction, growth velocity, and stretch.
  • Applying the vortex filament equation to generate generalized Hasimoto surfaces.
  • Investigating the geometric properties and conditions through theoretical analysis and illustrative examples.

Main Results:

  • The pseudo null growth model provides a framework for understanding curve evolution in Minkowski 3-space.
  • Generalized Hasimoto surfaces exhibit unique geometric structures.
  • Conditions for the formation and characteristics of these surfaces are established.

Conclusions:

  • The proposed pseudo null growth model and generalized Hasimoto surfaces offer new insights into geometric modeling.
  • The findings contribute to the understanding of differential geometry and mathematical physics applications.