Date of Award
1981
Degree Type
Report
Degree Name
Master of Science (MS)
Department
Mathematics and Statistics
Committee Chair(s)
Ian Anderson
Committee
Ian Anderson
Abstract
Many theorems in differential geometry which deal with the existence of certain geometrical structures or properties depend upon various existence and uniqueness theorems for differential equations. Because of its wide range of applications one of the most important of these theorems is the Frobenius Theorem for systems of total differential equations. There are four different forms of the Frobenius Theorem. In applications of the theorem one form is often preferable to the others. In this report we -shall prove the Frobenius Theorem, establish the equivalence of these various forms, and discuss a few applications.
Recommended Citation
Nagao, Hiroshi, "The Frobenius Theorem" (1981). All Graduate Plan B and other Reports, Spring 1920 to Spring 2023. 1197.
https://digitalcommons.usu.edu/gradreports/1197
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