The goal of Change Point Detection (CPD) is to identify sudden shifts in (usually temporal) sequential data. Recently, distribution-free CPD algorithms gained traction as an alternative to traditional statistical models, showing increased accuracy and generalization. However, most of the existing methods focus on time series with no spatial structure, or time series defined on flat spatial domains. Both settings are often limiting, as many real-world phenomena comprise time series defined on curved spatial domains. For this reason, in this paper, we introduce Manifold TIRE (ManTIRE), a novel variant of the renowned Time-Invariant REpresentation (TIRE) framework, able to perform CPD for univariate time series defined on curved domains - i.e., scalar fields on Riemann manifolds - from partial observations. The core elements of ManTIRE are Manifold Neural Networks, specific instances of geometric graph neural networks capturing the geometry of the underlying manifold.