Lorentz numbers are all couples $a + \tau b$ such that a , b are real numbers and $\tau^ 2 = 1$. We study functions over Lorentz numbers and their diÆerentiability. We obtain basic properties about regularity, an extension result of functions on manifolds and an implicit function theorem in the case of one or more variables. Then, we consider manifolds modelled on Lorentz numbers and, as a particular case, we obtain paracomplex manifolds.
On differentable functions over Lorentz numbers and their geometric applications
DI TERLIZZI, Luigia;
2014-01-01
Abstract
Lorentz numbers are all couples $a + \tau b$ such that a , b are real numbers and $\tau^ 2 = 1$. We study functions over Lorentz numbers and their diÆerentiability. We obtain basic properties about regularity, an extension result of functions on manifolds and an implicit function theorem in the case of one or more variables. Then, we consider manifolds modelled on Lorentz numbers and, as a particular case, we obtain paracomplex manifolds.File in questo prodotto:
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