A factorization of a super-conformal map

A super-conformal map and a minimal surface are factored into a product of two maps by modeling the Euclidean four-space and the complex Euclidean plane on the set of all quaternions. One of these two maps is a holomorphic map or a meromorphic map. These conformal maps adopt properties of a holomorphic function or a meromorphic function. Analogs of the Liouville theorem, the Schwarz lemma, the Schwarz-Pick theorem, the Weierstrass factorization theorem, the Abel-Jacobi theorem, and a relation between zeros of a minimal surface and branch points of a super-conformal map are obtained.Comment: 21 page

Curvature properties of some class of Minimal Hypersurfaces in Euclidean spaces

© 2015, University of Nis. All Rights Reserved. We determine curvature properties of pseudosymmetry type of some class of minimal 2-quasiumbilical hypersurfaces in Euclidean spaces En+1, n≥4. We present examples of such hypersurfaces. The obtained results are used to determine curvature properties of biharmonic hypersurfaces with three distinct principal curvatures in E5. Those hypersurfaces were recently investigated by Y. Fu in [38]

On riemann and weyl compatible tensors

We investigate semi-Riemannian manifolds satisfying some curvature conditions. Those conditions are strongly related to pseudosymmetry