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In this paper we prove a condition under which a hyperbolic starshaped set has a center of hyperbolic symmetry. We also give the definition of isometric diameters for a hyperbolic convex set, which behave similar to affine diameters for Euclidean convex sets. Using this concept, we give a definition of constant hyperbolic width and we prove that the only hyperbolic sets with constant hyperbolic width and with a hyperbolic center of symmetry are hyperbolic discs.
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참고문헌 (13)
참고문헌 신청
A. F. Beardon / 1995 / The Geometry of Discrete Groups / Springer-Verlag
B. V. Dekster / 1993 / Double normals characterize bodies of constant width in Riemannian manifolds, Geometric analysis and nonlinear partial differential equations (Denton,
G. D. Chakerian / 1983 / Convexity and its Applications / Birkh¨auser
H. Rademacher / 1957 / The Enjoyment of Mathematics / Princeton University Press
I. Yaglom / 1961 / Convex Figures / Holt Rinehart and Winston
B. V. Dekster / 1993 / Double normals characterize bodies of constant width in Riemannian manifolds, Geometric analysis and nonlinear partial differential equations (Denton,
G. D. Chakerian / 1983 / Convexity and its Applications / Birkh¨auser
H. Rademacher / 1957 / The Enjoyment of Mathematics / Princeton University Press
I. Yaglom / 1961 / Convex Figures / Holt Rinehart and Winston
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