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Second derivative of function evaluated along a curve on a Riemannian manifold

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#differential-geometry #riemannian-geometry #smooth-manifolds #curves #geodesic
22
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If $x_2(t)/x_1(t)=y_2(t)/y_1(t)$, then is $\vec Y(t)=(y_1(t),y_2(t))$ a reparametrization of $\vec X(t)=(x_1(t),x_2(t))$?

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#differential-geometry #curves #parametrization
44
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Normal of curvature of curves in a surface

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#differential-geometry #curves #curvature
79
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Differential of vector field

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#derivatives #differential-geometry #smooth-manifolds #curves #vector-fields
108
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Which curve is this, if any?

Published on
#curves #recursion
69
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Tangent vector fields imply tangent Lie bracket

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#ordinary-differential-equations #differential-geometry #solution-verification #curves #lie-derivative
54
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Continuous closed non intersecting curve which lies in bounded region but has an infinite length

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#complex-analysis #area #curves #plane-curves
62
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Is the relation between all equations and all curves in plane surjective?

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#real-analysis #curves #plane-geometry #plane-curves
43
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Linearly spacing points along non uniform curve

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#linear-algebra #graphing-functions #curves #least-squares
55
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Spatial curve with certain condition

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#geometry #differential-geometry #3d #curves
47
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Explicit curve with unbounded torsion

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#differential-geometry #curves
67
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Global sections of a curve compoare to global sections of the reduced curve

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#algebraic-geometry #curves #sheaf-theory #algebraic-curves
50
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Arclength parametrisation in 4D.

Published on
#curves #classical-mechanics #arc-length
40
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Must the orientation of a parameterized curve $\gamma:I\subseteq\mathbb{R}\to \mathbb{R}^n$ be in the direction of the increasing parameter?

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#multivariable-calculus #curves #line-integrals
66
Views

Intrinsic definition of arc length

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#differential-geometry #riemannian-geometry #curves

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