On space-like generalized constant ratio hypersufaces in Minkowski spaces

2016/03/03 by Mahmut Ergüt, Ergüt, Mahmut, Alev Kelleci +3
Mathematics · #53B25 (Secondary) #53C42 (Primary) #53D12 #Differential Geometry (math.DG) #FOS: Mathematics #math.DG #msc:53B25 #msc:53C42 #msc:53D12

paper · pdf · doi:10.48550/arxiv.1603.08415

Keywords: Generalized constant ratio hypersurfaces, Minkowski 3-space, space-like surfaces, flat surfaces

arxiv created 2018/11/08 · arxiv updated 2018/11/09

Abstract

A hypersurface in a Euclidean space 𝔼ⁿ⁺¹ is said to be a generalized constant ratio (GCR) hypersurface if the tangential part of its position vector is one of its principle directions. In this work, we move the study of generalized constant ratio hypersurfaces started in \cite% YuFu2014GCRS into the Minkowski space. First, we get some geometrical properties of non-degenerated GCR hypersurfaces in an arbitrary dimensional Minkowski space. Then, we obtain complete classification of GCR surfaces in the Minkowski 3-space. We also give some explicit examples.

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