caa a22 4500 463248031 CHVBK 20180405153331.0 cr unu---uuuuu 170326e20070801xx s 000 0 eng 10.1007/s10455-006-9054-4 doi (NATIONALLICENCE)springer-10.1007/s10455-006-9054-4 Slesar Vladimir Faculty of Mathematics and Computer Sciences, University of Craiova, 13, Al.I. Cuza st., 200585, Craiova, Romania aut Spectral sequences and taut Riemannian foliations [Elektronische Daten] [Vladimir Slesar] Using a relation between the terms of the spectral sequence of a Riemannian foliation and its adiabatic limit, we obtain Bochner type techniques for this special setting and, as a consequence, in the special case of a Riemannian flow we obtain vanishing conditions for the top dimensional group of the basic cohomology $$H_{b}^{q}(\mathcal{F})$$ -which is related to the property of being geodesible. We also extend a Weitzenböck type formula for the leafwise Laplacian and, for the particular class of compact foliations, we obtain a generalization of a result due to Ph. Tondeur, M. Min-Oo, and E. Ruh concerning the vanishing of the basic cohomology under the assumption that certain curvature operators are positive definite. In the final part we present an example. Springer Science + Business Media B.V., 2006 Riemannian foliation nationallicence Geodesic flow nationallicence Spectral sequences nationallicence Annals of Global Analysis and Geometry Kluwer Academic Publishers 32/1(2007-08-01), 87-101 0232-704X 32:1<87 2007 32 10455 https://doi.org/10.1007/s10455-006-9054-4 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s10455-006-9054-4 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Slesar Vladimir Faculty of Mathematics and Computer Sciences, University of Craiova, 13, Al.I. Cuza st., 200585, Craiova, Romania aut NATIONALLICENCE 773 0- Annals of Global Analysis and Geometry Kluwer Academic Publishers 32/1(2007-08-01), 87-101 0232-704X 32:1<87 2007 32 10455 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer