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On Strongly Convex Indicatrices in Minkowski Geometry

Published online by Cambridge University Press:  20 November 2018

Min Ji  and
Zhongmin Shen
Min Ji
Affiliation:
Graduate School at Beijing, University of Science and Technology of China and Institute of Mathematics, Academia Sinica, Beijing 100086, P.R. China, e-mail: jimin@math08.math.ac.cn
Zhongmin Shen
Affiliation:
Department of Mathematical Sciences, Indiana University-Purdue University, 402 N. Blackford Street, Indianapolis, IN 46202-3620, USA, e-mail: zshen@math.iupui.edu
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Abstract

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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.

Keywords

46B2053C2153A5552A2053B4053A35
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 45 , Issue 2 , 01 June 2002 , pp. 232 - 246
Copyright
Copyright © Canadian Mathematical Society 2002

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