In Star Trek, a geodesic fold is a temporary gateway through space. They can be created by firing a geodesic pulse, a verteron beam, into the magnetic field of a red giant star. As the geodesic fold opens, a corresponding fold will open in the magnetic field of another red giant, linking the two points. Geodesic folds, however, emit high levels of geodesic radiation, which standard Federation shields cannot withstand. Therefore, any ship attempting to pass through will have all organic tissue aboard liquefied.  In the Star Trek Voyager episode "Inside man", a Ferenggi created a geodesic fold at a red giant as part of a scheme to bring USS Voyager to the Alpha Quadrant, so that he could sell Seven of Nine's nanoprobes.

The term geodesic, in mathematics, is defined to be the shortest path between points on the space or curves whose tangent vectors remain parallel if they are transported along it. The term "geodesic" comes from geodesy, the science of measuring the size and shape of Earth; in the original sense, a geodesic was the shortest route between two points on the Earth's surface, namely, a segment of a great circle. Geodesics are of particular importance in general relativity, as they describe the motion of inertial test particles.

While there is certainly no known phenomena in real science known as a 'geodesic fold', it's principle certainly appears to be similar to that of a wormhole - a hypothetical topological feature of spacetime that is fundamentally a 'shortcut' through space and time. Spacetime can be viewed as a 2D surface, and when 'folded' over, a wormhole bridge can be formed (see Wormhole).

Free particle geodesics "fill" the light ray geodesic light cone at event e