Apparently, a T-shaped organism in a positively curved space can wiggle around in such a way as to translate itself across space, thereby achieving locomotion simply by changing its shape in a specific series are ways. I've seen a computer generated animation of this and it's actually pretty cool. It's said that this is possible in elliptical space because the notion of "center of mass" is ill-defined in such a space. What does this mean exactly? In what sense is the notion of "center of mass" not rigorously defined in curved space?