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Riemannian foliations of bounded geometry
Author(s) -
López Jesús A. Álvarez,
Kordyukov Yuri A.,
Leichtnam Eric
Publication year - 2014
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.201300211
Subject(s) - mathematics , bounded function , trace (psycholinguistics) , riemannian geometry , geometry , pure mathematics , foliation (geology) , mathematical analysis , geology , philosophy , linguistics , geochemistry , metamorphic rock
Continuing the study of bounded geometry for Riemannian foliations, begun by Sanguiao, we introduce a chart‐free definition of this concept. Our main theorem states that it is equivalent to a condition involving certain normal foliation charts. For this type of charts, it is also shown that the derivatives of the changes of coordinates are uniformly bounded, and there are nice partitions of unity. Applications to a trace formula for foliated flows will be given in a forthcoming paper.