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# On Strongly Convex Indicatrices in Minkowski Geometry

Published:2002-06-01
Printed: Jun 2002
• Min Ji
• Zhongmin Shen
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## Abstract

The geometry of indicatrices is the foundation of Minkowski geometry. A strongly convex indicatrix in a vector space is a strongly convex hypersurface. It admits a Riemannian metric and has a distinguished invariant---(Cartan) torsion. We prove the existence of non-trivial strongly convex indicatrices with vanishing mean torsion and discuss the relationship between the mean torsion and the Riemannian curvature tensor for indicatrices of Randers type.
 MSC Classifications: 46B20 - Geometry and structure of normed linear spaces 53C21 - Methods of Riemannian geometry, including PDE methods; curvature restrictions [See also 58J60] 53A55 - Differential invariants (local theory), geometric objects 52A20 - Convex sets in $n$ dimensions (including convex hypersurfaces) [See also 53A07, 53C45] 53B40 - Finsler spaces and generalizations (areal metrics) 53A35 - Non-Euclidean differential geometry

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