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To the question about the maximum principle for manifolds over local algebras

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Abstract

We consider manifolds over a local algebra A. We study basis functions of the canonical foliation which represent the real parts of A-differentiable functions. We prove that these are constant functions. We find the form of A-differentiable functions on some manifolds over local algebras, in particular, on compact manifolds. We obtain an estimate for the dimension of some spaces of 1-forms and analogs of the above results for the projective mappings of foliations.

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Authors and Affiliations

  1. Chebotarev Research Institute of Mathematics and Mechanics, Kazan’ State University, Russia

    T. I. Gaisin

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  1. T. I. Gaisin
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Original Russian Text Copyright © 2005 Ga\( \overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\smile}$}}{\imath} \)sin T. I.

Translated from Sibirski \( \overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\smile}$}}{\imath} \) Matematicheski \( \overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\smile}$}}{\imath} \) Zhurnal, Vol. 46, No. 1, pp. 79–89, January–February, 2005.

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Gaisin, T.I. To the question about the maximum principle for manifolds over local algebras. Sib Math J 46, 62–70 (2005). https://doi.org/10.1007/s11202-005-0006-1

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  • DOI: https://doi.org/10.1007/s11202-005-0006-1

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