TY - JOUR T1 - Convex Hull of Extreme Points in Flat Riemannian Manifolds AU - Mirzaie, Reza AU - Rezaie, Omid PY - 2022 DA - October Y2 - 2022 DO - 10.36890/iejg.1046707 JF - International Electronic Journal of Geometry JO - Int. Electron. J. Geom. PB - Kazım İlarslan WT - DergiPark SN - 1307-5624 SP - 178 EP - 182 VL - 15 IS - 2 LA - en AB - We show that convex hull of extreme points of a closed convex subset of a compact flat Riemannian manifold is equal to the subset itself. KW - Flat Reimannian manifold KW - convex subset KW - convex hull KW - extreme point CR - [1] Ballmann, W.: Lectures on Spaces of Nonpositive curvature. Brikhauser, Boston, Basel, Berlin, Stuttgart (1985). CR - [2] Bangert, V.: Totally convex sets in complete Riemannian manifolds. J. Differential Geometry. 16, 333-345 (1981). https://doi.org/10.4310/jdg/1214436108 CR - [3] Beltagy, M. Shenawy, S.: On the boundary of closed convex sets in En. arxiv:1301.0688v1 [math.MG] 4 Jan (2013). CR - [4] Bieberbach, L.: Über die Bewegungsgruppen der Euklidischen Räume II: Die Gruppen mit einem endlichen Fundamentalbereich. Mathematische Annalen. 72 400-412 (1912). https://doi.org/10.1007/BF01456724 CR - [5] Bredon, B.: Introduction to compact transformation groups. Acad Press. New york, London (1972). CR - [6] do Carmo, M. P.: Riemannian Geometry. Brikhauser, Boston, Basel, Berlin (1992). CR - [7] Munkres, J. R.: Topology; a First course. Prentic-Hall (1974). CR - [8] Lay, S. R.: Convex sets and their applications. John Wiley and Sons. Dekker, New York (1982). CR - [9] Shenawy, S.: Convex and Starshaped Sets in Manifolds without Conjugate Points. International Electronic Journal Of Geometry. Volume 12, no. 2, 223-228 (2019). https://doi.org/10.36890/iejg.628087 UR - https://doi.org/10.36890/iejg.1046707 L1 - https://dergipark.org.tr/en/download/article-file/2156492 ER -