Winding number and homotopy for quaternionic curves
Sergio Giardino
TL;DR
This paper introduces a quaternionic polar angle to define winding number and homotopy for quaternionic curves, enabling analysis of their global properties and applications in physics and analogies to plane curves.
Contribution
It presents a novel approach to quaternionic curves by defining a quaternionic polar angle, leading to new global invariants like winding number and homotopy.
Findings
Defined quaternionic polar angle for curves
Established global properties such as winding number and homotopy
Applications in physics and analogies to plane curves
Abstract
Following a recent approach to quaternionic curves, we defined the quaternionic polar angle that enabled us to define global properties of quaternionic curves, namely the winding number and the homotopy concept. The results admit various applications, including further analogies to plane curves, and physical applications.
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Taxonomy
TopicsAlgebraic and Geometric Analysis · Geometric Analysis and Curvature Flows · Mathematics and Applications