Golden Ratio, Affinor Structures, and Generalized Symmetric Spaces
УДК 514.1
Abstract
It is known that the most important affinor structures on smooth manifolds are almost complex structures, almost product structures, f-structures of Kentaro Yano, and some others. However, a new type of affinor structures was introduced and intensively discussed in differential geometry in the last decade. These are the so-called Golden structures first introduced by M. Crasmareanu and C.-E. Hretcanu using the well-known quadratic equation for the Golden ratio. Since then, a number of papers have been devoted to the study of the integrability of Golden structures, compatible Riemannian metrics and connections, submanifolds in such manifolds, etc. At the same time, invariant Golden structures on homogeneous manifolds have not appeared in these investigations. In this paper, a wide collection of invariant Golden structures on homogeneous generalized symmetric spaces is presented. More precisely, we obtained a complete description of all canonical Golden structures on homogeneous k-symmetric spaces. A remarkable feature of these structures is that all of them are invariant with respect to both the acting Lie group as well as the generalized symmetries of order k of homogeneous k-symmetric spaces.
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References
Crasmareanu M., Hretcanu C.-E. Golden differential geometry // Chaos, Solitons and Fractals. 2008. V. 38.
Hretcanu C.-E., Crasmareanu M. Applications of the Golden ratio on Riemannian manifolds // Turkish J. Math. 2009. V. 33.
Gezer A., Cengiz N., Salimov A. On integrability of Golden Riemannian structures // Turkish J. Math. 2013. V. 37.
Ozkan M. Prolongations of golden structures to tangent bundles // Differ. Geom. Dyn. Syst. 2014. V. 16.
Sahin B., Akyol M.A. Golden maps between golden Riemannian manifolds and constancy of certain maps // Math. Commun. 2014. V. 19, no. 2.
Etayo F., Santamaria R., Upadhyay A. On the geometry of almost Golden Riemannian manifolds // Mediterr. J. Math. 2017. V. 14, no. 5.
Erdem S. On product and golden structures and harmonicity // Turkish J. Math. 2018. V. 42, no. 2.
Goldberg S.I., Yano K. Polynomial structures on manifolds // Kodai Math. Sem. Rep. 1970. V. 22.
Goldberg S.I., Petridis N.C. Differentiable solutions of algebraic equations on manifolds // Kodai Math. Sem. Rep. 1973. V. 25.
Балащенко В.В., Степанов Н.А. Канонические аффинорные структуры классического типа на регулярных Φ-пространствах // Матем. сборник. 1995. T. 186, № 11.
Балащенко В.В., Никоноров Ю.Г., Родионов Е.Д., Славский В.В. Однородные пространства: теория и приложения : монография. Ханты-Мансийск, 2008.
Феденко А.С. Пространства с симметриями. Минск, 1977.
Ковальский О. Обобщенные симметрические пространства. М., 1984.
Степанов Н.А. Основные факты теории φ-пространств // Известия вузов. Математика. 1967. № 3.
Балащенко В.В., Дашевич О.В. Геометрия канонических структур на однородных Φ-пространствах порядка 4 // Успехи мат. наук. 1994. Т. 49, № 4.
Чурбанов Ю.Д. Геометрия однородных Φ-пространств порядка 5 // Известия вузов. Математика. 2002. № 5.
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