On a Variety of Algebraic Minimal Surfaces in Euclidean 4-Space

Minimal Surfaces in Euclidean Space

Characterizations of Slant Ruled Surfaces in the Euclidean 3-space

In this study, we give the relationships between the conical curvatures of ruled surfaces generated by the unit vectors of the ruling, central normal and central tangent of a ruled surface in the Euclidean 3-space E^3. We obtain differential equations characterizing slant ruled surfaces and if the reference ruled surface is a slant ruled surface, we give the conditions for the surfaces generate...

Minimal Surfaces in Euclidean Space Lecture Notes, Uab, Spring 1992

Mean Curvature One Surfaces in Hyperbolic Space, and Their Relationship to Minimal Surfaces in Euclidean Space

We describe local similarities and global differences between minimal surfaces in Euclidean 3-space and constant mean curvature 1 surfaces in hyperbolic 3-space. We also describe how to solve global period problems for constant mean curvature 1 surfaces in hyperbolic 3-space, and we give an overview of recent results on these surfaces. We include computer graphics of a number of examples.

On the Tangent Space to the Space of Algebraic Cycles on a Smooth Algebraic Variety

In this work we shall propose definitions for the tangent spaces TZ(X) and TZ(X) to the groups Z(X) and Z(X) of 0-cycles and divisors, respectively, on a smooth n-dimensional algebraic variety. Although the definitions are algebraic and formal, the motivation behind them is quite geometric and much of the text is devoted to this point. It is noteworthy that both the regular differential forms o...