We classify surfaces in 3-dimensional space forms which have all the local conformal invariants constant and show that compact 3-manifolds of nonzero constant sectional curvature admit no foliations by such surfaces.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-ap94-1-7,
author = {Adam Bartoszek and Pawe\l\ Walczak},
title = {Foliations by surfaces of a peculiar class},
journal = {Annales Polonici Mathematici},
volume = {93},
year = {2008},
pages = {89-95},
zbl = {1152.53021},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap94-1-7}
}
Adam Bartoszek; Paweł Walczak. Foliations by surfaces of a peculiar class. Annales Polonici Mathematici, Tome 93 (2008) pp. 89-95. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap94-1-7/