Put yoghurt in a bowl. Wash the cup, dry it and use it to measure the ingredients. Beat the eggs and icing sugar with the whisk of the hand mixer until creamy. Mix starch, flour, baking powder and grated coconut.
Stir yoghurt and oil into the egg mixture. Gradually add the flour mixture and mix. Pour into a greased, floured box form (25 cm long; 1.5 litres capacity). Bake in a preheated oven (electric cooker: 175 °C/ convection oven: 150 °C/ gas: level 2) for approx. 50 minutes.
In the meantime, wash the limes in hot water and rub them dry. Grate the zest of 2 limes thinly and squeeze the juice. Cut the remaining lime into slices. Caramelise the sugar. Add the juice and 2 tbsp. water and simmer gently to dissolve the caramel.
Add the lime slices and the grated zest to the lime syrup and leave to stand. Take out the cake, let it rest in the pan for a short time and turn it over. Prick the surface several times with a wooden skewer. Soak the cake in the syrup. Spread lime slices on the cake. Let the cake cool down