Nathaniel Bushek, Jeanne N. Clelland, “Geometry of Centroaffine Surfaces in <nobr>$\mathbb{R}^5$</nobr>”, SIGMA, 2015, Volume 11,001, 24 pp.

Geometry of Centroaffine Surfaces in $\mathbb{R}^5$

Nathaniel Bushek^a, Jeanne N. Clelland^b

^a Department of Mathematics, UNC - Chapel Hill, CB \# 3250, Phillips Hall, Chapel Hill, NC 27599, USA
^b Department of Mathematics, 395 UCB, University of Colorado, Boulder, CO 80309-0395, USA

Abstract: We use Cartan's method of moving frames to compute a complete set of local invariants for nondegenerate, 2-dimensional centroaffine surfaces in $\mathbb{R}^5 \setminus \{0\}$ with nondegenerate centroaffine metric. We then give a complete classification of all homogeneous centroaffine surfaces in this class.

Keywords: centroaffine geometry; Cartan's method of moving frames.

MSC: 53A15; 58A15

Received: August 23, 2014; in final form December 26, 2014; Published online January 6, 2015

Language: English

DOI: 10.3842/SIGMA.2015.001