Abstract:
The present paper investigates a class of twodimensional rational surfaces F in R^{4} whose tangent planes satisfy the following property: For any threespace E in R^{4} there exists a unique tangent plane T of F 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 R^{4} occur as special cases. This construction generalizes the concept of LNsurfaces in R^{3} to twodimensional surfaces in R^{4}.
Bibtex:
@inproceedings{peternellodehnalgenln08, author = "Martin Peternell and Boris Odehnal",
title = "On Generalized LNSurfaces in 4Space ",
booktitle = {{ISSAC} 2008: Intl.~Symposium on Symbolic Computation},
publisher = {ACM},
editor = "David Jeffrey",
url = "http://www.geometrie.tuwien.at/peternell/issac08_peternell.pdf",
year = 2008,
pages = "223230",
}

