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In this work, we develop a differential-geometric framework for superpolar geometries, extending the superelliptic structures introduced in previous studies to manifold structures generated by Gielis’ general superformula. A superpolar Riemannian structure is introduced through a compatible metric induced by the general superformula, and the resulting manifold structure and associated geometric properties are investigated. Within this framework, we construct superpolar lines, planes, and spheres and study various superpolar submanifolds, including conic submanifolds, spheres, rectifying submanifolds, and rectifying hypersurfaces. A fundamental feature of this framework is that curves and surfaces which, from the Euclidean viewpoint, may appear as squares, triangles, symmetric or asymmetric shapes, or even irregular forms with sharp points and corners, can be regarded intrinsically as circles and spheres with respect to the superpolar metric. In other words, structures that appear irregular or anisotropic in Euclidean geometry may correspond to regular geometric objects in their intrinsic geometry. Thus, the observed anisotropy is not an intrinsic property of the geometry, but rather a consequence of its Euclidean embedding.