IFLP   13074
INSTITUTO DE FISICA LA PLATA
Unidad Ejecutora - UE
congresos y reuniones científicas
Título:
Geodesic completeness of homogeneous affine surfaces
Autor/es:
GILKEY, PETER; PISANI, PABLO; D'ASCANIO, DANIELA; VALLE-REGUEIRO, XIAN
Lugar:
Cádiz
Reunión:
Workshop; II Joint Meeting Spain-Brazil in Mathematics; 2018
Institución organizadora:
RSME-SEMA-SBM-SBMAC
Resumen:
If gamma is a curve in an affine surface (M,abla), then the geodesic equation is ${ddot{gamma}}^{i} + Gamma_{jk}^{i}{dot{gamma}}^{j}{dot{gamma}}^{k} = 0$ for all i. There are 3 families of homogeneous affine surfaces. The Type A are the left invariant structures on the translation group R2, the Type B are the left invariant structures on the ax+b group, and the Type C arise as the underlying affine structure of a surface of constant sectional curvature. We discuss complete classification results for the geodesically complete Type A and partial results for the Type B surfaces. This is work in progess with Daniela D?Ascanio and Pablo Pisani (Dept. Fisica Universidad Nacional de la Plata, Argentina) and X. Valle-Regueiro (Universidade de Santiago, Spain).
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