The metric for a three-sphere is ds² = R² (d² + sin² § (d0² + sin² 0d²)) where ranges from 0 to 27, and §,0 range from 0 to T. a) Find the volume of the sphere b) find the first correction to the volume of a small sphere of radius r, when the space is the three-sphere of radius R instead of flat 3D Euclidean space

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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The metric for a three-sphere is
ds² = R² (d² + sin² (d0² + sin² 0do²))
where ranges from 0 to 2π, and §,0 range from 0 to T.
a) Find the volume of the sphere
b) find the first correction to the volume of a small sphere of radius r,
when the space is the three-sphere of radius R instead of flat 3D
Euclidean space
Transcribed Image Text:The metric for a three-sphere is ds² = R² (d² + sin² (d0² + sin² 0do²)) where ranges from 0 to 2π, and §,0 range from 0 to T. a) Find the volume of the sphere b) find the first correction to the volume of a small sphere of radius r, when the space is the three-sphere of radius R instead of flat 3D Euclidean space
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