An introduction to spectral and differential geometry in Carnot-Carathéodory spaces
Rumin, Michael
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Displaying similar documents to “Applications of spectral geometry to affine and projective geometry.”
An introduction to spectral and differential geometry in Carnot-Carathéodory spaces
κ-deformation, affine group and spectral triples
Bruno Iochum, Thierry Masson, Andrzej Sitarz (2012)
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A regular spectral triple is proposed for a two-dimensional κ-deformation. It is based on the naturally associated affine group G, a smooth subalgebra of C*(G), and an operator 𝓓 defined by two derivations on this subalgebra. While 𝓓 has metric dimension two, the spectral dimension of the triple is one. This bypasses an obstruction described in [35] on existence of finitely-summable spectral triples for a compactified κ-deformation.
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The use of one theorem of spectral analysis proved by Bordoni on a model of linear anisotropic beam proposed by the author allows the determination of the variation range of vibration frequencies of a beam in two typical restraint conditions. The proposed method is very general and allows its use on a very wide set of problems of engineering practice and mathematical physics.
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An up-spectral space need not be -spectral.
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