The software center shows F-Spot photo manager as software for the Gnome desktop. Is there an equivalent software for the Unity desktop?
Despite having "Unity" name written all over it, Unity is but a plugin for compiz and a bunch of customizations of a regular gnome desktop. The dash is Unity and replaces the Gnome shell, but most of the applications one runs (the status bar, the notifications, the control center, the screensaver, the file manager) are from Gnome.
Therefore, you can use F-Spot with good conscience.
However, the default application for managing and correcting photographs that comes with Ubuntu is called shotwell; note that it is also primarily Gnome.
Both Shotwell and F-spot are sufficiently similar to have sparked a vivid discussion about which one is better. F-Spot was criticized for lack of stability, and Shotwell for lack of features. See also this question.
Best try it for yourself.