Journal of the Ramanujan Mathematical Society

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Circumscribing Tubes and Two-Point Homogeneous Spaces


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1 Department of Mathematics, Katholieke Universiteit Leuven Celestijnenlaan 200b, B-3001, Leuven, Belgium
     

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First one derives a general formula for the volume of a tube about a curve in a two-point homogeneous space. The expression depends only on the length of the curve and the volume of a geodesic sphere. This leads to an expression for the volume of a socalled circumscribing tube. Then one investigates to what extent this expression for that volume is characteristic for two-point homogeneous spaces.
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  • Circumscribing Tubes and Two-Point Homogeneous Spaces

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Authors

L. Vanhecke
Department of Mathematics, Katholieke Universiteit Leuven Celestijnenlaan 200b, B-3001, Leuven, Belgium

Abstract


First one derives a general formula for the volume of a tube about a curve in a two-point homogeneous space. The expression depends only on the length of the curve and the volume of a geodesic sphere. This leads to an expression for the volume of a socalled circumscribing tube. Then one investigates to what extent this expression for that volume is characteristic for two-point homogeneous spaces.