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/