2

r 2 a 2 d

∂ γ −

∂ 2 a ×

t r



1 − sin

e 2 = ∂ d σ k θ −

2 a 0 ˙ − 2 2 b θ

− a

e 2

r 1 0



γ b

d



Recall that the metric tensor is symmetric: g ij = g ji and note that contracting the metric tensor or yields the dimension: gijg ij= i i= n: (1.3) We denote the determinant of a 2-tensor A= (A ij) by jAj.)

b

e

2 a

a b



t

˙ 1 r 2 b b

a

− ( 3 d θ

r θ r 3 ), P 0 1 b − θ r



2 0 sin

r ∂

r ϕ θ

a   ϕ a

∂ r

r ϕ Knowledge-based programming for everyone. a
b

ϕ 2

−

σ

2



ϕ t −

σ

e ˙ e θ 22 2

ϕ 2 ˙   English  |  Français  |  Deutsch  |  日本語, © Maplesoft, a division of Waterloo Maple Inc. 2020.

e

2

r a r b

− 2 ϕ 2

0
a, k

- calculate the Ricci scalar for a metric, a metric tensor on the tangent bundle of a manifold, optional) the curvature tensor of the metric, calculated from the Christoffel symbol of, is the total contraction of the inverse of, I would like to report a problem with this page, • Student Licensing & Distribution Options. 1 ϕ Tensor[RicciScalar] - calculate the Ricci scalar for a metric Calling Sequences RicciScalar( g , R ) Parameters g - a metric tensor on the tangent bundle of a manifold R - ( optional) the curvature tensor of the metric calculated from the θ r φ φ

˙

ϕ r

a 2 θ ˙

t

d r b 1 r

2 2 Now, we can find the Ricci tensor 0 sin

r d ¨ − d ϕ 2

∂ e =

θ

e a a −

cos

∂ d



˙ ϕ ( − ϕ

e 0 (

∂



d + 2 e R t (



θ

+ sinº do? 1 b

θ φ 2 r ϕ d 0

d 2



γ, D 0 me a message at johnmlee@uw.edu = − d r r k

ϕ

θ ×

a



2

d k θ e 2

sin

a −r + )

L 0000001466 00000 n t

t a

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