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The maximum principle for manifolds over a local algebra

Tagir I. Gaisin
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Abstract

Let $A$ be a finite-dimensional local commutative algebra over $R$, $\dim_RA=n$. In this work we consider compact manifolds over $A$, and prove that the real part of an $A$-differentiable function is constant. Also we find estimates for the dimensions of some spaces of 1-form.

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Tagir I. Gaisin. 2004-03-03. The maximum principle for manifolds over a local algebra. https://arxiv.org/abs/math/0402237

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