On the Tchebychev Vector Field in the Relative Differential Geometry

2015/11/29 by Stylianos Stamatakis, Stamatakis, Stylianos
Mathematics · Physics and Astronomy · #53A05 #53A07 #53A15 #53A40 #Advanced Differential Geometry Research #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Point processes and geometric inequalities

paper · pdf · doi:10.48550/arxiv.1512.00405

openalex publication_date 2015/11/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we deal with relative normalizations of hypersurfaces in the (n+1)-dimensional Euclidean space ℝⁿ⁺¹. Considering a relative normalization y of an hypersurface Φ we decompose the corresponding Tchebychev vector T in two components, one parallel to the Tchebychev vector T_EUK of the Euclidean normalization ξ and one parallel to the orthogonal projection y_T of y in the tangent hyperplane of Φ. We use this decomposition to investigate some properties of Φ, which concern its Gaussian curvature, the support function, the Tchebychev vector field etc.

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