Differential Geometry
# lemniscate Torus
$ S^1 \times S^1 $
$ sl \times S^1 $
$ sl \times S^1 $
# immersion
immerse : 浸す
~~~
M := {(x,y); x=a ,y=f(a)}
T(M)(a) := {(x,y) ; f'(a)(x-a) + f(a)} : tangent space at x = a
m : M -> N
D(m)(a) : T(M)(a) -> T(N)(m(a))
$ \forall a. $ D(m)(a) is injective,
m is Immersion
~~~
lemniscate is an immersion image ,
so the domain is mere
an ellipse.
so lemniscates might be mere the rendering problems ?