The algebraic surfaces of the minimal-maximal surfaces
Affiliation:
1. Bartın University, Faculty of Sciences, Department of Mathematics, Bartın, Turkey
Abstract
Considering soft computing, the Weierstrass data (??1/2, ?1/2) gives two
different minimal surface equations and figures. By using hard computing, we
give the family of minimal and spacelike maximal surfaces S(m,n) for natural
numbers m and n in Euclidean and Minkowski 3-spaces E3, E2,1, respectively.
We obtain the classes and degrees of surfaces S(m,n). Considering the
integral free form of Weierstrass, we define some algebraic functions for
S(m,n). Indicating several maximal surfaces of value (m, n) are algebraic,
we recall Weierstrass-type representations for maximal surfaces in E2,1, and
give explicit parametrizations for spacelike maximal surfaces of value (m,
n). Finally, we compute the implicit equations, degree, and class of the
spacelike maximal surfaces S(0,1), S(1,1) and S(2,1) in terms of their
cartesian or inhomogeneous tangential coordinates in E2,1.
Publisher
National Library of Serbia
Reference22 articles.
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