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Master's Dissertation
DOI
10.11606/D.45.2017.tde-05122017-104145
Document
Author
Full name
Artur Bicalho Saturnino
E-mail
Institute/School/College
Knowledge Area
Date of Defense
Published
São Paulo, 2017
Supervisor
Committee
Gorodski, Claudio (President)
Gozzi, Francisco Jose
Martin, Luiz Antonio Barrera San
Title in Portuguese
Curvatura extrínseca de órbitas de representações
Keywords in Portuguese
Ações Isométricas
Curvatura Extrínseca
Grupos de Lie
Representações Ortogonais
Abstract in Portuguese
Seja K um grupo de Lie compacto agindo na esfera unitária Sⁿ por isometrias. Mostramos como uma cota superior para as curvaturas principais de uma órbita dessa ação pode ser usada (mas não é suficiente) para encontrar uma cota inferior para o diâmetro do espaço de órbitas Sⁿ/K. Em seguida mostramos que existe uma órbita Kp com curvaturas principais majoradas por 4√ 14.
Title in English
Extrinsic curvature of orbits of representations
Keywords in English
Extrinsic Curvature
Isometric Actions
Lie Groups
Orthogonal Representations
Abstract in English
Let K be a compact Lie group acting on the unit sphere Sⁿ by isometries. We show how an upper bound on the principal curvatures of one orbit can be used (but is not sufficient) to obtain a lower bound for the diameter of the orbit space Sⁿ/K. Then we show that there is an orbit Kp with principal curvatures bounded from above by 4√ 14.
 
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Publishing Date
2017-12-05
 
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