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Complete Integrability of a Nonlinear Elliptic System, Generating Bi-umbilical Foliated Semi-symmetric Hypersurfaces in R^4 Пълна интегруемост на една нелинейна елиптична система, пораждаща би-омбилични фолирани полусиметрични хиперповърхнини в R^4

Kutev, Nikolai;  Milousheva, Velichka — 2010

Union of Bulgarian Mathematicians

Николай Кутев, Величка Милушева - Намираме експлицитно всичките би-омбилични фолирани полусиметрични повърхнини в четиримерното евклидово пространство R^4 We find explicitly all bi-umbilical foliated semi-symmetric hypersurfaces in the four- dimensional Euclidean space. *2000 Mathematics Subject Classification: 35A07, 35J60, 53A07, 53A10. The second author is partially supported by “L. Karavelov” Civil Engineering Higher School, Sofia, Bulgaria under Contract No 10/2009.

Invariants and Bonnet-type theorem for surfaces in ℝ4

Georgi Ganchev;  Velichka Milousheva — 2010

Open Mathematics

In the tangent plane at any point of a surface in the four-dimensional Euclidean space we consider an invariant linear map ofWeingarten-type and find a geometrically determined moving frame field. Writing derivative formulas of Frenet-type for this frame field, we obtain eight invariant functions. We prove a fundamental theorem of Bonnet-type, stating that these eight invariants under some natural conditions determine the surface up to a motion. We show that the basic geometric classes of surfaces...

Quasi-minimal rotational surfaces in pseudo-Euclidean four-dimensional space

Georgi Ganchev;  Velichka Milousheva — 2014

Open Mathematics

In the four-dimensional pseudo-Euclidean space with neutral metric there are three types of rotational surfaces with two-dimensional axis - rotational surfaces of elliptic, hyperbolic or parabolic type. A surface whose mean curvature vector field is lightlike is said to be quasi-minimal. In this paper we classify all rotational quasi-minimal surfaces of elliptic, hyperbolic and parabolic type, respectively.

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