Foliated Manifolds with Bundle-Like Metrics

Abstract

JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact support@jstor.org.

Arithmeticity of Holonomy Groups of Lie Foliations

“…In particular, if X is a Riemannian manifold and G is a group of isometries, g-is called a Riemannian foliation, and if X = G, a connected Lie group, then g-is called a Lie foliation, or more precisely, a G-foliation. These cases have been studied in [4,8,9,12,17,22], and elsewhere. By passing to a transverse orthogonal frame bundle, the study of Riemannian foliations can in most respects be reduced to the study of Lie foliations (see, e.g., [17]).…”

Energy–momentum tensor on foliations

“…The metric g M is said bundle-like in the sence of [27]. This definition is equivalent to the fact that the restriction h| Q is skew-symmetric.…”

Second-Order Geometric Flows on Foliated Manifolds

“…The definition of Riemannian foliation was introduced and firstly studied by B. Reinhart in [20] as a natural generalization of Riemannian submersions. Roughly speaking a foliation F on a manifold M is Riemannian if there exists a Riemannian metric on M such that the distance from one leaf of F to another is locally constant.…”