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What is the higher dimensional analogue for the arc of a circle?

I'd like to work with the set of all points lying within a certain distance of a given point on an n-sphere, and I'd like to describe these sets by the (generalised) solid angles which they subtend.

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A spherical wedge, or a spherical cap? – J. M. Aug 1 '12 at 2:33
Or hyperspherical, as the case may be. It's easy to denote it as an intersection of a ball and a sphere. – anon Aug 1 '12 at 2:38
@J.M. Make that an answer, would you please? – Rahul Aug 1 '12 at 2:43
up vote 1 down vote accepted

By request:

It seems you want either the spherical cap or the spherical wedge, or hyperspherical versions thereof.

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Thanks, just what I was looking for. Thanks also to anon. – Aug 1 '12 at 3:10

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