Date of Award
Master's Essay - Restricted
Master of Science (MS)
Differential Geometry is the study of the differentiable properties of curves and surfaces at a point. The properties of small segments of curves and surfaces are investigated, leading to the study of these properties in the large. In Michael Spivak's A Comprehensive Introduction to Differential Geometry, Volume I (Brandeis University, Lecture Notes), the author presents the groundwork for an analytical study of manifolds: tangent bundles, tensors, vector fields, differential forms, Riemannian metrics, and the equations of structure based on Lie groups. This paper will be a survey of the use of some of these structural techniques in presenting the geometric aspects of classical differential geometry.
Janik, Jacqueline C., "A Modern Approach to Classical Differential Geometry" (1972). Master's Essays (1922 - ). 1209.