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Growth functions of geodesic spheres

Title
Growth functions of geodesic spheres
Authors
안미선
Issue Date
1986
Department/Major
대학원 수학과
Keywords
geodesic spheres측지구 증가함수mathematics
Publisher
이화여자대학교 대학원
Degree
Master
Abstract
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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일반대학원 > 수학과 > Theses_Master
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