scholarly journals The singularities of the wave trace of the basic Laplacian of a Riemannian foliation

2007 ◽  
Vol 243 (1) ◽  
pp. 1-27 ◽  
Author(s):  
M.R. Sandoval
Keyword(s):  
Riemannian Foliation ◽  
Basic Laplacian ◽  
Wave Trace

The basic Laplacian of a Riemannian foliation

1996 ◽  
Vol 118 (6) ◽  
pp. 1249-1275 ◽  
Author(s):  
Efton Park ◽  
Ken Richardson
Keyword(s):  
Riemannian Foliation ◽  
Basic Laplacian

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.

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

?-Automorphisms of a Riemannian foliation

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

Evaluating Possibility of Registering Scattered Gravitational Radiation on Wormholes

2020 ◽  
pp. 89-102
Author(s):  
A.A. Kirillov ◽  
D.P. Krichevskiy
Keyword(s):  
Numerical Simulation ◽  
Gravitational Wave ◽  
Cross Section ◽  
Gravitational Radiation ◽  
Wave Amplitude ◽  
Spherically Symmetric ◽  
Curved Space ◽  
Klein Gordon ◽  
Wave Trace ◽  
Limiting Case

Possibility of experimental registration of gravitational radiation scattered on wormholes was evaluated. Scattered radiation registration could become the experimental evidence of the wormhole gas theory explaining the dark matter nature. The simplest model of the traversable static spherically symmetric wormhole was used, which is the limiting case for the Bronnikov --- Ellis wormhole. Equations for gravitational wave against the background of non-empty curved space--time were obtained in the gauge, where the trace of a gravitational wave is not equal to zero. It is shown that equation on the trace is reduced to the Klein --- Gordon --- Fock equation. Explicit expressions were obtained for the gravitational wave trace scattering cross section on a wormhole. It was assumed that the gravitational wave amplitude order was equal to its trace order, numerical simulation was carried out, and scattered gravitational radiation intensity and amplitude from wormholes on Earth were estimated. In the multiverse case, when the wormhole throat was leading to another universe, conclusion was made that it was currently impossible to register radiation scattered by wormholes taking into account the LIGO/VIRGO detector sensitivity

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.

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