scholarly journals Riemannian foliation with exotic tori as leaves

2019 ◽  
Vol 51 (4) ◽  
pp. 745-750
Author(s):  
F. Thomas Farrell ◽  
Xiaolei Wu
Keyword(s):  
Riemannian Foliation

scholarly journals Riemannian foliations with Ehresmann connection

2018 ◽  
Vol 20 (4) ◽  
pp. 395-407
Author(s):  
N. I. Zhukova
Keyword(s):  
Linear Connection ◽  
Riemannian Foliation ◽  
Minimal Set ◽  
Foliated Manifold ◽  
Trivial Bundle ◽  
Riemannian Foliations ◽  
Ehresmann Connection ◽  
The Family ◽  
Leaf Space ◽  
Complete Riemannian Manifolds

It is shown that the structural theory of Molino for Riemannian foliations on compact manifolds and complete Riemannian manifolds may be generalized to a Riemannian foliations with Ehresmann connection. Within this generalization there are no restrictions on the codimension of the foliation and on the dimension of the foliated manifold. For a Riemannian foliation (M,F) with Ehresmann connection it is proved that the closure of any leaf forms a minimal set, the family of all such closures forms a singular Riemannian foliation (M,F¯¯¯¯). It is shown that in M there exists a connected open dense F¯¯¯¯-saturated subset M0 such that the induced foliation (M0,F¯¯¯¯|M0) is formed by fibers of a locally trivial bundle over some smooth Hausdorff manifold. The equivalence of some properties of Riemannian foliations (M,F) with Ehresmann connection is proved. In particular, it is shown that the structural Lie algebra of (M,F) is equal to zero if and only if the leaf space of (M,F) is naturally endowed with a smooth orbifold structure. Constructed examples show that for foliations with transversally linear connection and for conformal foliations the similar statements are not true in general.

?-Automorphisms of a Riemannian foliation

1995 ◽  
Vol 13 (3) ◽  
pp. 281-288 ◽  
Author(s):  
Hong Kyung Pak
Keyword(s):  
Riemannian Foliation

scholarly journals A characterization of harmonic foliations by the volume preserving property of the normal geodesic flow

2002 ◽  
Vol 29 (10) ◽  
pp. 573-577
Author(s):  
Hobum Kim
Keyword(s):  
Geodesic Flow ◽  
Riemannian Foliation ◽  
Volume Form ◽  
Normal Connection ◽  
Riemannian Volume ◽  
Canonical Metric ◽  
Normal Geodesic ◽  
Harmonic Foliations ◽  
Volume Preserving

We prove that a Riemannian foliation with the flat normal connection on a Riemannian manifold is harmonic if and only if the geodesic flow on the normal bundle preserves the Riemannian volume form of the canonical metric defined by the adapted connection.

ON THE CURVATURE GROUPS OF A RIEMANNIAN FOLIATION

2011 ◽  
Vol 63 (3) ◽  
pp. 585-603
Author(s):  
S. Dragomir ◽  
R. Petit
Keyword(s):  
Riemannian Foliation

scholarly journals Riemannian homogeneous foliations without holonomy

1975 ◽  
Vol 83 ◽  
pp. 197-201 ◽  
Author(s):  
Robert A. Blumenthal
Keyword(s):  
Riemannian Foliation ◽  
Natural Projection ◽  
Fibre Space

Let M be a compact connected C∞ manifold with a smooth Riemannian foliation ℱ. That is, (M, ℱ) admits a bundle-like metric in the sense of [7]. In [4] it is shown that if all leaves of ℱ are closed without holonomy, then the space of leaves M/ℱ of the foliation is a manifold and the natural projection M → M/ℱ is a locally trivial fibre space. In the present work we show that for certain of the Riemannian homogeneous foliations, holonomy is the only obstruction to the foliation being a fibration.

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