## Geometry, Algebra and Applications: From Mechanics to CryptographyMarco Castrillón López, Luis Hernández Encinas, Pedro Martínez Gadea, Ma Eugenia Rosado María 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. |

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### Contents

1 | |

On the 1+3 Threading of Spacetime | 13 |

Local Structure of SelfDual Gradient Yamabe Solitons | 25 |

The Prescribed Curvature Problem in Low Dimension | 36 |

EulerPoincaré Reduction by a Subgroup of Symmetries as an Optimal Control Problem | 49 |

Morse Families and Lagrangian Submanifolds | 65 |

Properties and Applications | 79 |

Rotation Minimizing Vector Fields and Frames in Riemannian Manifolds | 91 |

Classes of Nonlinear Filters for Stream Ciphers | 107 |

Implementation of Cryptographic Algorithms for Elliptic Curves | 120 |

Supermanifolds Symplectic Geometry and Curvature | 135 |

Prime Submodules and Symmetric Algebras | 147 |

Application to Cybersecurity of the Stability Theory of the Systems of Ordinary Differential Equations | 157 |

On the Nontriviality of the EightForm τ4ω on Manifolds with a Spin9Structure | 170 |

Flaws in the Application of Number Theory in Key Distribution Schemes for Multicast Networks | 181 |

EinsteinHilbert Lagrangian Induced on the Linear Frame Bundle | 188 |

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Algorithm Castrill´on L´opez Castrillón López coefficient cohomology computer worm coordinates coset cotangent bundle cryptosystem defined denote differential dS(B elliptic curve equations Euler–Poincaré fiber Frenet frame function Geom Geometry gradient Yamabe soliton Hence homogeneous Lorentzian homogeneous quaternionic Kähler International Publishing Switzerland isometry isotropic Jaime Muñoz Masqué Kähler structures Lemma Levi-Civita connection Lie g locally Lorentzian metrics malware Math Mathematics & Statistics Mechanics to Cryptography minimal prime ideal nonlinear filters notation obtain operations Phys polynomial Proceedings in Mathematics Proposition pseudo-Riemannian Publishing Switzerland 2016 quaternionic quaternionic Kähler structures R-module representation resp Ricci tensor Riemannian manifolds RM frame RM vector field safe primes scalar curvature scalar multiplication self-dual sequence signature soliton space spacetime Spain e-mail spatial Springer International Publishing Springer Proceedings strong prime submodule supermanifold symmetric algebra symplectic form tangent tensor field Theorem vector field