On the magnitude of spheres, surfaces and other homogeneous spaces

Details On the magnitude of spheres, surfaces and other homogeneous spaces On the magnitude of spheres, surfaces and other homogeneous spaces

2010-05-21

arxiv.org/abs/1005.4041v1

Mathematics

Differential Geometry

20 pages

Scientific paper

In this paper we define the magnitude of metric spaces using measures rather than finite subsets as had been done previously and show that this agrees with earlier work with Leinster in arXiv:0908.1582. An explicit formula for the magnitude of an n-sphere with its intrinsic metric is given. For an arbitrary homogeneous Riemannian manifold the leading terms of the asymptotic expansion of the magnitude are calculated and expressed in terms of the volume and total scalar curvature of the manifold. In the particular case of a homogeneous surface the form of the asymptotics can be given exactly up to vanishing terms and this involves just the area and Euler characteristic in the way conjectured for subsets of Euclidean space in previous work.

Affiliated with

Also associated with

No associations

Rating

On the magnitude of spheres, surfaces and other homogeneous spaces does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with On the magnitude of spheres, surfaces and other homogeneous spaces, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On the magnitude of spheres, surfaces and other homogeneous spaces will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-340374