Abstract. We study foliations of space forms by complete hypersurfaces, under some mild conditions on its higher order mean curvatures. In particular, in Euclidean space we obtain a Bernstein-type theorem for graphs whose mean and scalar curvature do not change sign but may otherwise be nonconstant. We also establish the nonexistence of foliations of the standard sphere whose leaves are complete and have constant scalar curvature, thus extending a theorem of Barbosa, Kenmotsu and Oshikiri. For the more general case of r-minimal foliations of the Euclidean space, possibly with a singular set, we are able to invoke a theorem of Ferus to give conditions under which the nonsigular leaves are foliated by hyperplanes.

The genus Physalaemus Fitzinger, 1826 is composed by 46 species occurring from north to southern South America, east of the Andes (Frost 2015). Physalaemus albifrons is morphologically differentiated from the other species mainly due to the presence of a second tarsal tubercle located nearly the tibio-tarsal articulation (Bokermann 1966). Physalaemus albifrons occurs in Brazil from north of the State of Maranhão through the states of Piauí, Ceará, Bahia, Paraíba, Pernambuco, and Alagoas, being its more austral occurrence in the State of Minas Gerais (Frost 2015). The advertisement call of P. albifrons was described by Bokermann (1966); however, the description needs improvement by applying new technologies, which we provide herein.