We introduce a conceptual geometric framework in which the Uni- verse is represented as a closed three-dimensional spatial hypersurface embed- ded in a higher-dimensional ambient space. No four-dimensional spacetime manifold is assumed at a fundamental level. Instead, cosmological time is in- troduced as an ordering parameter labeling successive geometric configurations of the hypersurface during a persistent global expansion process. Within this representation, expansion is treated as a continuous and global tendency that acts everywhere on the hypersurface. Gravitational phenomena are not attributed to a fundamental interaction nor to a local suppression of expansion. Rather, they are interpreted as geometric effects arising from how this global expansion is locally accommodated when the hypersurface contains regions of rigidity or geometric constraint. In such regions, expansion continues but cannot be realized homogeneously, leading to the emergence of extrinsic concavities and to geodesic focusing in the induced intrinsic geometry. Strongly constrained configurations may give rise to horizon-like structures and causal disconnection for observers confined to the hypersurface, provid- ing a geometric representation of black-hole-like behavior without invoking spacetime singularities. The proposed framework does not aim to replace the established formalisms of general relativity or standard cosmology. It is in- stead intended as a representational and intuitive geometric picture, offering an alternative perspective on the relationships between expansion, gravitation, and causal structure.