SOME PROBLEMS REGARDING THE SPECTRA OF HODGE-DE RHAM OPERATORS

SOME PROBLEMS REGARDING THE SPECTRA OF HODGE-DE RHAM OPERATORS

The smooth and continuous dependence on the Riemannian metric of the eigenvalues of the Hodge-de Rham operators and its consequences

LAP Lambert Academic Publishing ( 24.02.2010 )

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Spectral geometry deals with the survey of these natural, differential operators'' spectrums and among other things it tries to emphasize geometrical and topological properties of a manifold that can be recuperated from the spectrums. The present work is going to approach several issues referring to the spectrums of Hodge-de Rham operators on closed Riemannian manifolds. The author of this paper is going to discuss the continuous dependence on the Riemannian metrics on a smooth and closed differential manifold of the eigenvalues of the Hodge-de Rham operators and its restrictions regarding the exact, differential form spaces and consequences of such feature. Moreover, by using J. Wenzelburger''s idea [80], [81], we are going to prove that the eigenvalues of the Hodge-de Rham operators even smoothly depend on the Riemannian metrics on a smooth, closed, differential manifold if the Fréchet smooth manifold canonical structure is taken into consideration in the space of all Riemannian metrics with such a manifold.

Kitap detayları:

ISBN-13:

978-3-8383-4816-2

ISBN-10:

3838348168

EAN:

9783838348162

Kitabın dili:

English

Yazar:

Albici Mihaela

Sayfa sayısı:

140

Yayın tarihi:

24.02.2010

Kategori:

Geometri