Locally symmetric Finsler spaces in negative curvature |
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| Institution: | 1. School of Information and Control Engineering,Qingdao University of Technology, Qingdao 266525, PR China;2. Key Laboratory of Measurement and Control of Complex Systems of Engineering (Southeast University), Ministry of Education, Nanjing, Jiangsu 210096, PR China;3. College of Electrical and Electronic Engineering, Shandong University of Technology, Zibo, Shandong 255000, PR China;4. School of Automation, Southeast University, Nanjing, Jiangsu 210096, PR China |
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| Abstract: | É. Cartan introduced in 1926 the Riemannian locally symmetric spaces, as the spaces whose curvature tensor is parallel. They also owe their name to the fact that, for each point, the geodesic reflexion is a local isometry. The aim of this Note is to announce a strong rigidity result for Finsler spaces. Namely, we show that a negatively curved locally symmetric (in the first sense above) Finsler space is isometric to a Riemann locally symmetric space. |
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