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Structure of graphs of suspended foliations
Journal of Mathematical Sciences. 2022. Vol. 261. No. 3. P. 410–425.
Zhukova N. I., Chubarov G. V.
We study the graph G(F, Q) of a foliation F with Ehresmann connection Q. We prove that for any suspended foliation (M,F) the induced foliation on the graph G(F, Q) is also suspended. We describe the structure of the graph G(F, Q), as well as leaves of the induced foliation. We show that the induced foliation is a suspended foliation with the same
transversal manifold and the same structure group as the original foliation.
Keywords: надстроечное слоение,график слоенияsuspended foliation graph of a foliationtransversal manifoldтрансверсальное многообразие
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Flamarion M. V., Pelinovsky E., Chaos, Solitons and Fractals 2026 Vol. 213 No. 2 Article 119245
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Added: October 8, 2026
Люксембург А. А., УРСС, 2005.
Изучается возможность автоматизированного построения математических теорий. Рассматривается дедуктивная система, основанная на языке логики предикатов первого порядка, объектами системы являются математические выражения или формулы, которые описывают математические объекты или их свойства. В дедуктивной системе выводятся математические определения и теоремы. Для доказательства теорем используются методы автоматического доказательства. Разработан алгоритм, выводящий часть формул системы. Для решения задачи используется аппарат математической ...
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