Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 11 (2015), 001, 24 pages      arXiv:1408.4088      https://doi.org/10.3842/SIGMA.2015.001

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

Nathaniel Bushek a and 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

Received August 23, 2014, in final form December 26, 2014; Published online January 06, 2015

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.

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

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