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The volume of geodesic disks in a Riemannian manifold. (English) Zbl 0586.53006
Let M denote an analytic Riemannian manifold of dimension $$>2$$. For every unit vector $$x\in T_ mM$$ and sufficiently small radius r the authors call $D^ x_ m(r)=\exp_ m\{y\in T_ mM| \| y\| \leq r\quad and\quad y\perp x\}$ a geodesic disc. It is the purpose of the paper to provide complete formulas for the (n-1)-dimensional volume $$V^ x_ m(r)$$ of $$D^ x_ m(r)$$ if M is a two-point homogeneous space, and to show that these spaces are characterized by the functions $$(m,x,r)\mapsto V^ x_ m(r)$$.
Reviewer: H.Reckziegel

##### MSC:
 53B20 Local Riemannian geometry
##### Keywords:
geodesic disc; volume; two-point homogeneous space
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##### References:
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