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math.GM2014
Kaehler Algebra: Idempotents for Solutions with Symmetry in Metric Spaces
Jose G. Vargas
With his Clifford algebra of differential forms, Kaehler's algebra addresses the overlooked manifestation of symmetry in the solutions of exterior systems. In this algebra, solutio…
math.GM2014
Helmholtz-Hodge Theorems: Unification of Integration and Decomposition Perspectives
Jose G. Vargas
We develop a Helmholtz-like theorem for differential forms in Euclidean space using a uniqueness theorem similar to the one for vector fields. We then apply it to Riemannia…
math.GM2014
Helmholtz Theorem for Differential Forms in 3-D Euclidean Space
Jose G. Vargas
There are significant differences between Helmholtz and Hodge's decomposition theorems, but both share a common flavor. This paper is a first step to bring them together. We here p…