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Full-Text Articles in Algebraic Geometry
Early Investigations In Conformal And Differential Geometry, Raymond T. Walter
Early Investigations In Conformal And Differential Geometry, Raymond T. Walter
Inquiry: The University of Arkansas Undergraduate Research Journal
The present article introduces fundamental notions of conformal and differential geometry, especially where such notions are useful in mathematical physics applications. Its primary achievement is a nontraditional proof of the classic result of Liouville that the only conformal transformations in Euclidean space of dimension greater than two are Möbius transformations. The proof is nontraditional in the sense that it uses the standard Dirac operator on Euclidean space and is based on a representation of Möbius transformations using 2x2 matrices over a Clifford algebra. Clifford algebras and the Dirac operator are important in other applications of pure mathematics and mathematical physics, …
Where Does It All End? Boundaries Beyond Euclidean Space, Jonathan Thompson
Where Does It All End? Boundaries Beyond Euclidean Space, Jonathan Thompson
Inquiry: The University of Arkansas Undergraduate Research Journal
No abstract provided.