We construct complete nonorientable minimal surfaces whose Gauss map omits two points of RP 2 . This result proves that Fujimoto’s theorem is sharp in nonorientable case.

One of the earliest applications of modern integrable systems theory (or “soliton theory”) to differential geometry was the solution of the problem of finding all constant mean curvature (CMC) tori in R3 (and therefore, by taking the Gauss map, finding all non-conformal harmonic maps from a torus to S2). At its simplest level this proceeds from the recognition that the Gauss-Codazzi equations o...

The paper concerns the problem of correct curvatures estimates directly from polygonal meshes. We present a new algorithm that allows the construction of unambiguous Gauss maps for a large class of polyhedral surfaces, including surfaces of non-convex objects and even non-manifold surfaces. The resulting Gauss map provides shape recognition and curvature characterisation of the polyhedral surfa...

We introduce the generalized helical hypersurface having a space-like axis in five-dimensional Minkowski space. compute first and second fundamental form matrices, Gauss map, shape operator matrix of hypersurface. Additionally, we curvatures by using Cayley–Hamilton theorem. Moreover, give some relations for mean Gauss–Kronecker Finally, obtain Laplace–Beltrami

We study mirror symmetry of Calabi-Yau manifolds within the framework of the Gauss-Manin system. Applying the flat coordinates to the Gauss-Manin system for the periods, we derive differential equations for the mirror map in addition to the ordinary Picard-Fuchs equations for the periods. These equations are obtained for a class of one-parameter models and a two-parameter model of Fermat type C...