Canad. Math. Bull. 45(2002), 232-246
Printed: Jun 2002
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.
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