Date of Award

1981

Degree Type

Report

Degree Name

Master of Science (MS)

Department

Mathematics and Statistics

First Advisor

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.

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