On generalized ln-surfaces in 4-space

Authors:
Martin Peternell;Boris Odehnal
Affiliations:
University of Technology, Vienna, Austria;University of Technology, Vienna, Austria
Venue:
Proceedings of the twenty-first international symposium on Symbolic and algebraic computation
Year:
2008

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Abstract

The present paper investigates a class of two-dimensional rational surfaces φ in R4 whose tangent planes satisfy the following property: For any three-space E in R4 there exists a unique tangent plane T of φ which is parallel to E. The most interesting families of surfaces are constructed explicitly and geometric properties of these surfaces are derived. Quadratically parameterized surfaces in R4 occur as special cases. This construction generalizes the concept of LN-surfaces in R3 to two-dimensional surfaces in R4.