Immanants of hyperbolic triangles

• Ano de defesa: 2023
• Autor(a) principal: Cussy, Omar Chavez
• Tipo de documento: Tese
• Tipo de acesso: Acesso aberto
• Idioma: eng
• Instituição de defesa: Biblioteca Digitais de Teses e Dissertações da USP
• Palavras-chave em Português: Área de triângulos hiperbólicos; Area of hyperbolic triangles; Imanantes de matrizes 3×3; Immanants of matrices of order 3 x 3; Plano hiperbólico real; Real hyperbolic plane
• Link de acesso: https://www.teses.usp.br/teses/disponiveis/55/55135/tde-10012025-171657/

We determine relations between triangles in the hyperbolic plane and the immanants of doubly stochastic Gram matrices associated with the vertices. Firstly, we prove that the three immanants of the doubly stochastic Gram matrix of a hyperbolic triangle determine the triangle modulo isometries. Secondly, we provide a formula for the area of a hyperbolic triangle in terms of the corresponding immanants. Finally, we show that the area of a hyperbolic triangle with one ideal vertex is determined by any pair of immanants and we explain in which immanants the area function is monotone.