Existence and uniqueness for Legendre curves
By Tomonori Fukunaga, Masatomo Takahashi. 2012
97 citations recorded by the source corpus.
We give a moving frame of a Legendre curve (or, a frontal) in the unit tangent bundle and define a pair of smooth functions of a Legendre curve like as the curvature of a regular plane curve. It is quite useful to analyse the Legendre curves. The existence and uniqueness for Legendre curves hold similarly to the case of regular plane curves. As an application, we consider contact between Legendre curves and the arc-length parameter of Legendre immersions in the unit tangent bundle.
Subfields: Applied Mathematics, Astronomy and Astrophysics, Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/76d48d5cc51d485f83fe90850dce65d0f5f7e7fb
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In Applied Mathematics
In Astronomy and Astrophysics
In Geometry and Topology
Citations in the corpus
- Framed curves in the Euclidean space (2016, background): “By (6) and a direct calculation, we have”
- Evolutes and involutes of fronts in the Euclidean plane (Pursuit of the Essence of Singularity Theory) (2013, unknown): “…is pictured as follows: . . . $arrow \int_{t_{0}}^{t}(\int_{t_{0}}^{t}\beta(t)dt)dtarrow\int_{t_{0}}^{t}\beta(t)dtarrow\beta(t)arrow\frac{d}{dt}\beta(t)arrow\frac{d^{2}}{dt^{2}}\beta(t)arrow\cdots$ This is corresponding to the relationship between the differential and integral in classical calculus.”
- Involutes of fronts in the Euclidean plane (2013, unknown): “7 ([8]) Let (γ, ν) and (γ̃, ν̃) : I → R(2) × S(1) be congruent as Legendre curves.”