# Covariant Derivative of a Field along a Curve

Covariant Derivative of a Field along a Curve

This Demonstration gives a visual representation of the covariant derivative of a field along a curve , induced by a field , where is a Peano surface with parametric equations given by the chart

X(t)

α(t)=σ(u(t),v(t))

Y:SS

T

p

S

σ(u,v)=(u,v,(2-v)(v-))

2

u

2

u

This covariant derivative has been computed from its representation in terms of the given chart, the field and the corresponding Christoffel symbols:

X(t)

D

t

1

Γ

11

1

Γ

12

1

Γ

12

1

Γ

22

σ

u

2

Γ

11

2

Γ

12

2

Γ

12

2

Γ

22

σ

v

where are the coefficients of .

a(t),b(t)

X(t)=a(t)+b(t)

σ

u

σ

v