Multilinear evolution equations for time-harmonic flows in conformally flat manifolds

DOI10.1088/0264-9381/13/7/001zbMATH Open0857.58008arXivhep-th/9604033OpenAlexW1993216459MaRDI QIDQ4887507

Publication date: 10 March 1997

Published in: Classical and Quantum Gravity (Search for Journal in Brave)

Abstract: It is shown that time-harmonic hypersurface motions in various, conformally flat, N-dimensional manifolds admit a multilinear description, dL/dt={ L, M_1, ... , M_{N-2} }, automatically generating infinitely many conserved quantities, as well as leading to new (integrable) matrix equations. Interestingly, the conformal factor can be changed without changing L.

Full work available at URL: https://arxiv.org/abs/hep-th/9604033

zbMATH Keywords

conservation laws conformally flat manifolds hypersurface flows

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35) Global Riemannian geometry, including pinching (53C20) Equations in function spaces; evolution equations (58D25)

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