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SPECIAL CLASSES OF MERIDIAN SURFACES IN THE FOUR-DIMENSIONAL EUCLIDEAN SPACE
GANCHEV, GEORGI,MILOUSHEVA, VELICHKA Korean Mathematical Society 2015 대한수학회보 Vol.52 No.6
Meridian surfaces in the Euclidean 4-space are two-dimensional surfaces which are one-parameter systems of meridians of a standard rotational hypersurface. On the base of our invariant theory of surfaces we study meridian surfaces with special invariants. In the present paper we give the complete classification of Chen meridian surfaces and meridian surfaces with parallel normal bundle.
Aleksieva, Yana,Ganchev, Georgi,Milousheva, Velichka Korean Mathematical Society 2016 대한수학회지 Vol.53 No.5
We develop an invariant local theory of Lorentz surfaces in pseudo-Euclidean 4-space by use of a linear map of Weingarten type. We find a geometrically determined moving frame field at each point of the surface and obtain a system of geometric functions. We prove a fundamental existence and uniqueness theorem in terms of these functions. On any Lorentz surface with parallel normalized mean curvature vector field we introduce special geometric (canonical) parameters and prove that any such surface is determined up to a rigid motion by three invariant functions satisfying three natural partial differential equations. In this way we minimize the number of functions and the number of partial differential equations determining the surface, which solves the Lund-Regge problem for this class of surfaces.
SPECIAL CLASSES OF MERIDIAN SURFACES IN THE FOUR-DIMENSIONAL EUCLIDEAN SPACE
Georgi Ganchev,Velichka Milousheva 대한수학회 2015 대한수학회보 Vol.52 No.6
Meridian surfaces in the Euclidean 4-space are two-dimensional surfaces which are one-parameter systems of meridians of a standard rotational hypersurface. On the base of our invariant theory of surfaces we study meridian surfaces with special invariants. In the present paper we give the complete classification of Chen meridian surfaces and meridian surfaces with parallel normal bundle.
MERIDIAN SURFACES IN <sup>4</sup> WITH POINTWISE 1-TYPE GAUSS MAP
Arslan, Kadri,Bulca, Betul,Milousheva, Velichka Korean Mathematical Society 2014 대한수학회보 Vol.51 No.3
In the present article we study a special class of surfaces in the four-dimensional Euclidean space, which are one-parameter systems of meridians of the standard rotational hypersurface. They are called meridian surfaces. We show that a meridian surface has a harmonic Gauss map if and only if it is part of a plane. Further, we give necessary and sufficient conditions for a meridian surface to have pointwise 1-type Gauss map and find all meridian surfaces with pointwise 1-type Gauss map.
MERIDIAN SURFACES IN E4 WITH POINTWISE 1-TYPE GAUSS MAP
Kadri Arslan,Betul Bulca,Velichka Milousheva 대한수학회 2014 대한수학회보 Vol.51 No.3
In the present article we study a special class of surfaces in the four-dimensional Euclidean space, which are one-parameter systems of meridians of the standard rotational hypersurface. They are called meridian surfaces. We show that a meridian surface has a harmonic Gauss map if and only if it is part of a plane. Further, we give necessary and sufficient conditions for a meridian surface to have pointwise 1-type Gauss map and find all meridian surfaces with pointwise 1-type Gauss map.
Yana Aleksieva,Georgi Ganchev,Velichka Milousheva 대한수학회 2016 대한수학회지 Vol.53 No.5
We develop an invariant local theory of Lorentz surfaces in pseudo-Euclidean 4-space by use of a linear map of Weingarten type. We find a geometrically determined moving frame field at each point of the surface and obtain a system of geometric functions. We prove a fundamental existence and uniqueness theorem in terms of these functions. On any Lorentz surface with parallel normalized mean curvature vector field we introduce special geometric (canonical) parameters and prove that any such surface is determined up to a rigid motion by three invariant functions satisfying three natural partial differential equations. In this way we minimize the number of functions and the number of partial differential equations determining the surface, which solves the Lund-Regge problem for this class of surfaces.