Search results for "geodeesi"

showing 2 items of 2 documents

Hyperbolisen geometrian analyyttisiä malleja

2014

Tässä tutkielmassa esitellään viisi erilaista Riemannin monistoa, jotka toimivat hyperbolisen geometrian analyyttisinä malleina. Geometria voidaan karkeasti jakaa kahteen eri tapaukseen, euklidiseen ja epäeuklidiseen. Euklidisessa geometriassa pätee Eukleideen geometrian viides aksiooma, paralleeliaksiooma. Näin ei kuitenkaan ole laita hyperbolisessa geometriassa, joka luokitellaan epäeuklidiseksi geometriaksi. Analyyttisellä geometrialla taas tarkoitetaan koordinaatistoon sidottua geometriaa. Tässä tapauksessa nämä geometrian mallit ovat topologisia 2-ulotteisia pintoja euklidisessa avaruudessa. Lisäksi tutkielman malleissa hyödynnetään näille pinnoille määriteltyä sileää differentiaalirak…

differentiaaligeometriametriikkageodeesimonistogeometria

researchProduct

Injectivity results for the geodesic ray transform

2017

integraaligeometriageodeesitinversio-ongelmat

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