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Home New examples of zero mean curvature surfaces in the three-dimensional anti de-Sitter space

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New examples of zero mean curvature surfaces in the three-dimensional anti de-Sitter space

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Identifier	Thesis 2233
Author	LeMay, Steven Robert, 1983-
Title	New examples of zero mean curvature surfaces in the three-dimensional anti de-Sitter space
Publisher	Central Connecticut State University
Date	2012
Resource Type	Master's Thesis
Notes	This work deals with the construction of zero mean curvature surfaces in the three dimensional anti de-Sitter space. The method that was used was to look for examples that can be described using polynomial equations. More precisely, we are looking for "algebraic" examples of zero mean curvature surfaces. Success was found in finding new examples. Actually the author proved that if we used some polynomial equations previously discovered by Blaine Lawson to study a similar problem in the three dimensional sphere, these equations will also produce examples with zero mean curvature in the three dimensional anti de-Sitter space. This is considered the main result of the thesis. The family of examples that were found is so rich that it shows the existence of algebraic examples of any order; that is, examples produced with equations involving a polynomial of any desire degree. This thesis is written to be as self-contained as possible. In regard with the method used to prove the main result, two different approaches are explained to prove that a particular surface has zero mean curvature. One of them uses a parametrization of the surface and the other uses the polynomial that describes the surface. Even though both methods were thoroughly studied in the thesis, the former one was used to prove the main result
Subject	Curvature -- Mathematical models Surfaces of constant curvature Mathematics Mathematical analysis
Department	Department of Mathematical Sciences
Advisor	Perdomo, Oscar
Type	Text
Digital Format	application/pdf
Language	eng
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New examples of zero mean curvature surfaces in the three-dimensional anti de-Sitter space

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