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Master's Dissertation
DOI
https://doi.org/10.11606/D.45.2001.tde-20220712-115532
Document
Author
Full name
José Carlos Corrêa Eidam
E-mail
Institute/School/College
Knowledge Area
Date of Defense
Published
São Paulo, 2001
Supervisor
Title in Portuguese
O teorema do índice espectral para sistemas de Morse-Sturm
Keywords in Portuguese
Geometria Diferencial
Abstract in Portuguese
não disponível
Title in English
not available
Abstract in English
We consider a Morse-Sturm system in Rn whose coefficient matrix is symmetric with respect to a (non necessary positive definite) nondegenerate symmetric bilinear form on Rn. The main motivation for studying such systems comes from semi-Riemannian geometry, where the Morse-Sturm system is obtained from the Jacobi equation along a geodesic by writing the equation in terms of a parallely transported basis of the tangent bundle along the geodesic. Two integer numbers are naturally associated to such systems: the Maslov index, that gives a sort of algebraic count of the conjugate instants, and the spectral index, that gives an algebraic count of the negative eigenvalues of the corresponding second order differential operator. In this thesis we prove taht these two integer numbers are equal, in the case of Riemannian geometry, this equality is precisely the Morse Index Theorem
 
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Publishing Date
2022-07-13
 
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