Geometry, algebra and applications : from mechanics to cryptography ; in honor of Jaime Muñoz Masqué

This volume collects contributions written by different experts in honor of Prof. Jaime Muñoz Masqué. It covers a wide variety of research topics, from differential geometry to algebra, but particularly focuses on the geometric formulation of variational calculus; geometric mechanics and field theories; symmetries and conservation laws of differential equations, and pseudo-Riemannian geometry of homogeneous spaces. It also discusses algebraic applications to cryptography and number theory. It offers state-of-the-art contributions in the context of current research trends. The final result is a challenging panoramic view of connecting problems that initially appear distant. Front Matter....Pages i-xii A Survey on Homogeneous Structures on the Classical Hyperbolic Spaces....Pages 1-12 On the \((1+3)\) Threading of Spacetime....Pages 13-24 Local Structure of Self-Dual Gradient Yamabe Solitons....Pages 25-35 The Prescribed Curvature Problem in Low Dimension....Pages 37-48 Euler–Poincaré Reduction by a Subgroup of Symmetries as an Optimal Control Problem....Pages 49-63 Morse Families and Lagrangian Submanifolds....Pages 65-78 Special Primes: Properties and Applications....Pages 79-90 Rotation Minimizing Vector Fields and Frames in Riemannian Manifolds....Pages 91-100 Local Anomaly Cancellation and Equivariant Cohomology of Jet Bundles....Pages 101-106 Classes of Nonlinear Filters for Stream Ciphers....Pages 107-119 Implementation of Cryptographic Algorithms for Elliptic Curves....Pages 121-133 Supermanifolds, Symplectic Geometry and Curvature....Pages 135-146 Prime Submodules and Symmetric Algebras....Pages 147-156 Application to Cybersecurity of the Stability Theory of the Systems of Ordinary Differential Equations....Pages 157-169 On the Non-triviality of the Eight-Form \(\tau _4(\omega )\) on Manifolds with a \(\mathrm {Spin}(9)\) -Structure....Pages 171-179 Flaws in the Application of Number Theory in Key Distribution Schemes for Multicast Networks....Pages 181-187 Einstein–Hilbert Lagrangian Induced on the Linear Frame Bundle....Pages 189-198