Related papers: The Research on Rotational Surfaces in pseudo Eucl…

We define general rotational surfaces of elliptic and hyperbolic type in the pseudo-Euclidean 4-space with neutral metric which are analogous to the general rotational surfaces of C. Moore in the Euclidean 4-space. We study Lorentz general…

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…

We give the classification of constant mean curvature rotational surfaces of elliptic, hyperbolic, and parabolic type in the four-dimensional pseudo-Euclidean space with neutral metric.

In this work, we study some classes of rotational surfaces in the pseudo-Euclidean space $\mathbb{E}^4_t$ with profile curves lying in 2-dimensional planes. First, we determine all such surfaces in the Minkowski 4-space $\mathbb{E}^4_1$…

In this paper, we study rotational surfaces of elliptic, hyperbolic and parabolic type with pointwise 1-type Gauss map which have spacelike profile curve in four dimensional pseudo Euclidean space E4-2 and obtain some characterizations for…

In this work, we study a class of rotational surfaces in the pseudo-Euclidean space $\mathbb{E}_2^4$ whose profile curves lie in two-dimensional planes. We solve the differential equation that characterizes the rotational surfaces with zero…

In this paper, Clairaut's theorem is expressed on the surfaces of rotation in semi Euclidean 4-space. Moreover, the general equations of time-like geodesic curves are characterized according to the results of Clairaut's theorem on the…

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 classified…

In this paper, we study general rotational surfaces in the 4- dimensional pseudo-Euclidean space E4-2 and obtain a characterization of flat general rotation surfaces with pointwise 1-type Gauss map in E4-2 and give an example of such…

We study hypersurfaces in the pseudo-Euclidean space $\mathbb{E}^{n+1}_s$, which write as a warped product of a $1$-dimensional base with an $(n-1)$-manifold of constant sectional curvature. We show that either they have constant sectional…

In the present study we consider the generalized rotational surfaces in Euclidean spaces. Firstly, we consider generalized spherical curves in Euclidean $(n+1)-$space $\mathbb{E}^{n+1}$. Further, we introduce some kind of generalized…

We apply the invariant theory of surfaces in the four-dimensional Euclidean space to the class of general rotational surfaces with meridians lying in two-dimensional planes. We find all minimal super-conformal surfaces of this class.

In the present paper we study the problem of constructing a family of surfaces (surface pencils) from a given curve in 4-dimensional Euclidean space $\mathbb{E}^{4}$. We have shown that generalized rotation surfaces in $\mathbb{E}^{4}$ are…

We consider a special class of spacelike surfaces in the Minkowski 4-space which are one-parameter systems of meridians of the rotational hypersurface with timelike or spacelike axis. We call these surfaces meridian surfaces of elliptic or…

We give a classification of rotational cmc surfaces in non-Euclidean space forms in terms of explicit parametrizations using Jacobi elliptic functions. Our method hinges on a Lie sphere geometric description of rotational linear Weingarten…

In this paper we review some author's results about Weingarten surfaces in Euclidean space $\r^3$ and hyperbolic space $\h^3$. We stress here in the search of examples of linear Weingarten surfaces that satisfy a certain geometric property.…

In the present paper we consider a special class of spacelike surfaces in the Minkowski 4-space which are one-parameter systems of meridians of the rotational hypersurface with timelike or spacelike axis. They are called meridian surfaces…

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…

General rotational surfaces as a source of examples of surfaces in the four-dimensional Euclidean space have been introduced by C. Moore. In this paper we consider the analogue of these surfaces in the Minkowski 4-space. On the base of our…

We study invariant surfaces generated by one-parameter subgroups of simply and pseudo isotropic rigid motions. Basically, the simply and pseudo isotropic geometries are the study of a three-dimensional space equipped with a rank 2 metric of…