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Growth functions of geodesic spheres
- Growth functions of geodesic spheres
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- 대학원 수학과
- geodesic spheres; 측지구 증가함수; mathematics
- 이화여자대학교 대학원
- Let M be an analytic Riemannian manifold of dimension n. For small r>0, denote by Sm(r) the (n-1)-dimensional volume of a geodesic sphere Gm(r) of radius r with center m. Then the growth function A(s) of Gm(r) is given by A(s)=Sm(r+s) for small s≥0. We characterize the space of constant curvature by the equations A"(s)+C(s)A(s)=0 for all Gm(r) or
A'''(s)+C (s)A''(s)+C (s)A' (s)+C (s)A(s)=0 for all Gm(r).
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