doi:10.1016/j.geomphys.2023.104899engDe Lucas, JavierRivas, XavierVilariño, SilviaZawora, Bartosz M.On k-polycosymplectic Marsden–Weinstein reductionsART-2023-134568We review and slightly improve the known k-polysymplectic Marsden–Weinstein reduction theory by removing some technical conditions on k-polysymplectic momentum maps by developing a theory of affine Lie group actions for k-polysymplectic momentum maps, removing the necessity of their co-adjoint equivariance. Then, we focus on the analysis of a particular case of k-polysymplectic manifolds, the so-called fibred ones, and we study their k-polysymplectic Marsden–Weinstein reductions. Previous results allow us to devise a k-polycosymplectic Marsden–Weinstein reduction theory, which represents one of our main results. Our findings are applied to study coupled vibrating strings and, more generally, k-polycosymplectic Hamiltonian systems with field symmetries. We show that k-polycosymplectic geometry can be understood as a particular type of k-polysymplectic geometry. Finally, a k-cosymplectic to ℓ-cosymplectic geometric reduction theory is presented, which reduces, geometrically, the space-time variables in a k-cosymplectic framework. An application of this latter result to a vibrating membrane with symmetries is given.2023http://zaguan.unizar.es/record/12757310.1016/j.geomphys.2023.104899http://zaguan.unizar.es/record/127573oai:zaguan.unizar.es:127573info:eu-repo/grantAgreement/ES/DGA/E48-20Rinfo:eu-repo/grantAgreement/ES/DGA/E48-23Rinfo:eu-repo/grantAgreement/ES/MICINN/PID2021-125515NB-C22JOURNAL OF GEOMETRY AND PHYSICS 191 (2023), 104899 [36 pp.]byhttp://creativecommons.org/licenses/by/3.0/es/info:eu-repo/semantics/openAccess