Geometric Model of Stellar Velocities in Spiral Galaxies: An Alternative Interpretation of Galactic Rotation Curves

This work presents a geometric model of stellar velocities in spiral galaxies. The proposed approach investigates whether the observed flattening of galactic rotation curves can be partially described through the geometry of stellar trajectories. The model introduces an effective trajectory geometry parameter b(r) and an invariant parameter K, leading to the relation between stellar velocity and spiral geometry. In this framework, deviations from circular motion are interpreted as a possible geometric contribution to the observed velocity profile. The model is applied to selected Milky Way rotation curve data, where the derived b(r) profile increases with galactic radius. The results suggest a possible connection between spiral structure and stellar velocity distribution. This work is presented as a theoretical investigation and requires further verification using extended observational datasets from different types of spiral galaxies.