We give an estimate of the Gauss curvature for minimal surfaces in Rm whose Gauss map omits more than m(m + 1)/2 hyperplanes in P(C).

The combinatorial Ricci curvature of Forman, which is defined at the edges of a CW complex, and which makes use of only the face relations of the cells in the complex, does not satisfy an analog of the Gauss-Bonnet Theorem, and does not behave analogously to smooth surfaces with respect to negative curvature. We extend this curvature to vertices and faces in such a way that the problems with co...

In this work we extend the Weierstrass representation for maximal spacelike surfaces in the 3-dimensional Lorentz–Minkowski space to spacelike surfaces whose mean curvature is proportional to its Gaussian curvature (linear Weingarten surfaces of maximal type). We use this representation in order to study the Gaussian curvature and the Gauss map of such surfaces when the immersion is complete, p...

We derive the equations of Gauss and Weingarten for a non-degenerate hypersurface of a semi-Riemannian manifold admitting a semi-symmetric metric connection, and give some corollaries of these equations. In addition, we obtain the equations of Gauss curvature and Codazzi-Mainardi for this non-degenerate hypersurface and give a relation between the Ricci and the scalar curvatures of a semi-Riema...

The objective of this paper is to construct and investigate smooth orientable surfaces in RN −1 by analytical methods. The structural equations of surfaces in connection with CPN−1 sigma models on Minkowski spacetime are studied in detail. This is carried out using a moving frame adapted to the surface immersed in su(N) algebra. The first and second fundamental forms of the surface as well as t...

This paper shows how the Gauss-Mainardi-Codazzi equations can be reinterpreted in terms of variations of curvature with respect to arc-length along lines of curvature. Secondly, it reviews the frame-and-position matching method for surface synthesis. Thirdly, it brings these two ideas together to show that frame and position matching for an infinitesimal patch are exactly equivalent to the Gaus...

We give an estimate of the Gauss curvature for minimal surfaces in R m whose Gauss map omits more than m(m + 1)=2 hyperplanes in P m?1 (C).