The Integrability Tensor for Bundle-Like Foliations
- 1 March 1982
- journal article
- Published by JSTOR in Transactions of the American Mathematical Society
- Vol. 270 (1) , 333-339
- https://doi.org/10.2307/1999776
Abstract
A certain function is introduced which is useful in the study of a bundle-like foliation on a Riemannian manifold. Under the assumption that the leaves are totally geodesic, the Laplacian of this function is computed along a leaf. From this computation a sufficient condition is provided for the ambient manifold to be locally isometric to a product.Keywords
This publication has 7 references indexed in Scilit:
- The Quantitative Theory of FoliationsCBMS Regional Conference Series in Mathematics, 2007
- A Remark on the Bochner Technique in Differential GeometryProceedings of the American Mathematical Society, 1980
- Totally geodesic foliationsJournal of Differential Geometry, 1980
- Riemannian submersions with totally geodesic fibersJournal of Differential Geometry, 1975
- Transformation Groups in Differential GeometryPublished by Springer Nature ,1972
- The fundamental equations of a submersion.The Michigan Mathematical Journal, 1966
- Foliated Manifolds with Bundle-Like MetricsAnnals of Mathematics, 1959