TL;DR
This paper extends the Frenet formulas from three-dimensional space to its tangent space, providing a comprehensive mathematical framework for analyzing lifted curves in higher-dimensional spaces.
Contribution
It introduces the vertical, complete, and horizontal lifts of Frenet formulas from R3 to TR3, expanding the tools for differential geometry analysis.
Findings
Derived explicit formulas for lifted Frenet frames
Established the relationships between original and lifted Frenet formulas
Enhanced understanding of curve behavior in tangent bundle spaces
Abstract
In this study, we conclude the vertical, complete and horizontal lifts of Frenet formulas given by (1) and defined on space R3 to its tangent space TR3 = R6.
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Taxonomy
TopicsHistory and Theory of Mathematics