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- W2567508377 abstract "Complex holomorphic functions are defined using a complex derivative. In higher dimensions the meaningful generalization of complex derivative is not straight forward. Sudbery defined a derivative for quaternion regular functions using differential forms. Gurlebeck and Malonek generalized that for monogenic functions. In this paper we find similar characterizations for k-hypermonogenic functions which are holomorphic functions based on the Riemannian metric $$begin{aligned} ds^{2}=frac{dx_{0}^{2}+dx_{1}^{2}+dx_{2}^{2}}{x_{2}^{2k}}. end{aligned}$$When (k=0), we obtain the hypercomplex derivative by Gurlebeck and Malonek. Just like in the complex case derivative of k-hypermonogenic is the usual partial derivative with respect to the first coordinate." @default.
- W2567508377 created "2017-01-06" @default.
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- W2567508377 date "2016-12-30" @default.
- W2567508377 modified "2023-10-07" @default.
- W2567508377 title "Quaternionic k-Hyperbolic Derivative" @default.
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- W2567508377 doi "https://doi.org/10.1007/s11785-016-0630-8" @default.
- W2567508377 hasPublicationYear "2016" @default.
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