This paper presents explicit equations over Q for 32 extremal semistable elliptic K3 surfaces. They are realized as pull-back of non-semi-stable extremal rational elliptic surfaces via base change. Together with work of J. Top and N. Yui which exhibited the same procedure for the semi-stable extremal rational elliptic surfaces, this exhausts this approach to produce extremal semi-stable ellipti...

Aspects of the properties, enumeration and construction of points on diagonal and Hermitian surfaces have been considered extensively in the literature and are further considered here. The zeta function of diagonal surfaces is given as a direct result of the work of Wolfmann. Recursive construction techniques for the set of rational points of Hermitian surfaces are of interest. The relationship...

Among geometrically rational surfaces, del Pezzo surfaces of degree 2 over a field k containing at least one point are arguably the simplest that are not known to be unirational over k. Looking for k-rational curves on these surfaces, we extend some earlier work of Manin on this subject. We then focus on the case where k is a finite field, where we show that all except possibly three explicit d...

A surface in homogenous space Sol is said to be an invariant surface if it is invariant under some of the two 1-parameter groups of isometries of the ambient space whose fix point sets are totally geodesic surfaces. In this work we study invariant surfaces that satisfy a certain condition on their curvatures. We classify invariant surfaces with constant mean curvature and constant Gaussian curv...

Bonnet surfaces, i.e. surfaces in Euclidean 3-space, which admits a one-parameter family of isometries preserving the mean curvature function, can be described in terms of solutions of some special Painlev e equations. The goal of this work is to use the well-known Schlesinger transformations for solutions of Painlev e VI equations to create new Bonnet surfaces from a known one.

In this paper, we classify surface at a constant distance from the edge of regression on translation surfaces of Type 1 in the three dimensional simply isotropic space I^1_3 satisfying some algebraic equations in terms of the coordinate functions and the Laplacian operators with respect to the first, the second and the third fundamental form of the surface. We also give explicit forms of these ...

the main issues about relation between climate and relief in the romanian geomorphological literature follow three directions of research: the description of pleistocene glacial and pleistocene-holocene periglacial landforms in the carpathians; the direct analysis of climate?s role in landform development; the integration of separate works and findings in a synthetic morphodynamic system applic...

in this paper, we study cyclic surfaces in 5 1 e generated by homothetic motions of a lorentziancircle. the properties of these cyclic surfaces up to first order are investigated. we show that, as it is shown ine5 , cyclic 2-surfaces in 5 1 e , in general, are contained in canal hypersurfaces. finally, we give an example.

We address the problem of texture mapping implicit surfaces. Recent work in providing 2D mappings for implicit surfaces maps points from an auxiliary parametric (support) surface to the implicit surface. In this work we extend this method by observing that all commonly used skeletal elements are easily parameterized and can be used as their own support surfaces. In areas of a surface defined by...