Baron von Munchahausen and the cat: Swimming in curved space

Cats fall on their feet, but Baron von Munchhausen could not have saved himself by pulling on his hair. Why can cats rotate without angular momentum while the Baron can not translate without momentum?  This is because Newton law says that,  in the absence of external forces, the center remains at rest. As we shall see, this law can be bypassed in a curved space. It is therefore possible for the Baron to swim in empty curved space.