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RIGID BODY EQUATIONS ON SPACES OF PSEUDO-DIFFERENTIAL OPERATORS WITH RENORMALIZED TRACE

Abstract : We equip the regular Fréchet Lie group of invertible, odd-class, classical pseudodifferential operators Cl 0, * odd (M, E)-in which M is a compact smooth manifold and E a (complex) vector bundle over M-with pseudo-Riemannian metrics, and we use these metrics to introduce a class of rigid body equations. We prove the existence of a metric connection, we show that our rigid body equations determine geodesics on Cl 0, * odd (M, E), and we present rigorous formulas for the corresponding curvature and sectional curvature. Our main tool is the theory of renormalized traces of pseudodifferential operators on compact smooth manifolds.
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https://hal.archives-ouvertes.fr/hal-03194881
Contributor : Jean-Pierre Magnot Connect in order to contact the contributor
Submitted on : Friday, April 9, 2021 - 8:23:47 PM
Last modification on : Wednesday, October 20, 2021 - 3:19:02 AM
Long-term archiving on: : Monday, July 12, 2021 - 9:24:30 AM

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rigidbodyv12.pdf
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  • HAL Id : hal-03194881, version 1

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Jean-Pierre Magnot, Enrique Reyes. RIGID BODY EQUATIONS ON SPACES OF PSEUDO-DIFFERENTIAL OPERATORS WITH RENORMALIZED TRACE. 2021. ⟨hal-03194881⟩

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