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 SM ISO690:2012DAMIAN, Florin. Hyperbolic manifolds built on the geometries of their cusps or submanifolds. In: Mathematics and Information Technologies: Research and Education, Ed. 2023, 26-29 iunie 2023, Chişinău. Chişinău: 2023, p. 23. ISBN 978-9975-62-535-7. |
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| Mathematics and Information Technologies: Research and Education 2023 | ||||||
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Conferința "Mathematics and Information Technologies: Research and Education" 2023, Chişinău, Moldova, 26-29 iunie 2023 | ||||||
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We describe geometric methods that allow to build and investigate hyperbolic manifolds of dimensions 3, 4 and 5, with certain predefined properties, such as cusps geometry, the geometry of a totally geodesic submanifold, etc. Some result of these constructions look like as a generalization of 2-dimensional pants. Also we use these examples and methods of metric reconstruction to obtain non-face-to-face incidence schemes for fundamental polyhedra. As a result, new manifolds and some exotic tilings on universal coverage are obtained. The talk will be focused on the transfer of methods of discrete geometry to topology and vice versa. |
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