The Fowler-Nordheim (FN) theory is extended to include a potential distribution outside an axisymmetric ellipsoid and a wall with a semi-elliptical shape. The tips of nanometric radii are considered. The variation in field emission over the surface is accounted for by an effective emission area. The FN slopes are found to be markedly larger in comparison with those predicted by the standard FN theory. Analysis of experimentally observed slopes can provide information about geometrical characteristics of emitters. It is shown that for wall-like emitters the geometrical effects are less pronounced in comparison with the axisymmetric emitters.