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Doctoral Thesis
DOI
https://doi.org/10.11606/T.45.1990.tde-20210728-235557
Document
Author
Full name
Rosa Maria dos Santos Barreiro Chaves
E-mail
Institute/School/College
Knowledge Area
Date of Defense
Published
São Paulo, 1989
Supervisor
Title in Portuguese
Alguns aspectos locais envolventes de n-esferas a dois parâmetros em uma forma especial
Keywords in Portuguese
Geometria Diferencial
Abstract in Portuguese
não disponível
Title in English
not available
Abstract in English
In this we are mainly concerned with the study of (special) 2-parameter envelopes of n-spheres 'M POT.N' (n'MAIOR IGUAL'4) in a simply connected space forms 'Q IND.C POT.N+1' (c=0, 1 or -1) which satisfy the weingarten relation a+bh+ck=o between the mean curvature h and the gauss-kronnecker curvature k of 'M POT.N'SETA'Q IND.C POT.N+1', where a, b and c are real constants, such a relation includes the case h = constant. We obtain some examples of those objects as well some non-existence results. We also study the possibility of a 2-parameter envelope of n-spheres 'M POT.N' in 'H POT.N+1' (case c=-1) be isometrically immersed into 'R POT.N+2' with everywhere zero normal curvature tensor. In our approach, the focal set of the envelope plays a fundamental role in the characterization of the envelope, in the construction of examples and in the proofs of results
 
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Publishing Date
2021-07-28
 
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