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Zachowanie geodezyjne i przechylenia przestrzeni hiperbolicznej
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ISBN10: 6208464307
ISBN13: 9786208464301
Publisher: Wydawnictwo Nasza Wiedza
Published: Sep 27 2025
Pages: 124
Weight: 0.39
Height: 0.29 Width: 6.00 Depth: 9.00
Language: Polish
ISBN13: 9786208464301
Publisher: Wydawnictwo Nasza Wiedza
Published: Sep 27 2025
Pages: 124
Weight: 0.39
Height: 0.29 Width: 6.00 Depth: 9.00
Language: Polish
Prezentowana praca dotyczy geometrii dwuwymiarowych hiperbolicznych (wyposażonych w metrykę o stalej ujemnej krzywiźnie) rozmaitości i bada przechylenia w hiperbolicznej n-przestrzeni o dowolnym wymiarze za pomocą politopów. W części pierwszej wprowadzamy nową metodę (metodę kolorowych multilateralów) do opisu globalnego zachowania geodezyjnego na dowolnych hiperbolicznych rozmaitościach o wymiarze dwa. Najlepiej zachowującymi się przechylami są przechyly twarzą w twarz przez wypukle wielościany. Szczególnie interesujące są przechyly w hiperbolicznej n-przestrzeni. W części drugiej glówne wyniki tej publikacji są uzyskane dla przechylów (izościennych, nieizościennych, twarzą w twarz, nie twarzą w twarz) w hiperbolicznej n-przestrzeni o dowolnym wymiarze dla dowolnego, () przez zwarte i nie zwarte polytopy i opisujemy ich dyskretne grupy izometrii i wlasności. Szczególnie ważne są grupy bezskrętne.
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