Submaximal metric projective and metric affine structures

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• 作者：Boris Kruglikov ; Vladimir Matveev
• 关键词：primary ; 53A20 ; 53A15 ; secondary ; 53B10 ; 53B05
• 刊名：Differential Geometry and its Applications
• 出版年：March, 2014
• 年：2014
• 卷：33
• 期：supp_S
• 页码：70-80
• 全文大小：320 K

文摘

We prove that the next possible dimension after the maximal for the Lie algebra of local projective symmetries of a metric on a manifold of dimension is if the signature is Riemannian or , if the signature is Lorentzian and , and elsewise. We also prove that the Lie algebra of local affine symmetries of a metric has the same submaximal dimensions (after the maximal ) unless the signature is Riemannian and , in which case the submaximal dimension is .