217 research outputs found
Sobolev Metrics on Diffeomorphism Groups and the Derived Geometry of Spaces of Submanifolds
Given a finite dimensional manifold , the group
of diffeomorphism of which fall
suitably rapidly to the identity, acts on the manifold of submanifolds
on of diffeomorphism type where is a compact manifold with . For a right invariant weak Riemannian metric on
induced by a quite general operator
, we
consider the induced weak Riemannian metric on and we compute its
geodesics and sectional curvature. For that we derive a covariant formula for
curvature in finite and infinite dimensions, we show how it makes O'Neill's
formula very transparent, and we use it finally to compute sectional curvature
on .Comment: 28 pages. In this version some misprints correcte
A common generalization of the Fr\"olicher-Nijenhuis bracket and the Schouten bracket for symmetry multi vector fields
There is a canonical mapping from the space of sections of the bundle to . It is shown that
this is a homomorphism on \Gamma(ST\ M)\Omega(T^\ast M;T(T^\ast M))$.Comment: 14 pages, AMSTEX, LPTHE-ORSAY 94/05 and ESI 70 (1994
Completely integrable systems: a generalization
We present a slight generalization of the notion of completely integrable
systems to get them being integrable by quadratures. We use this generalization
to integrate dynamical systems on double Lie groups.Comment: Latex, 15 page
Construction of completely integrable systems by Poisson mappings
Pulling back sets of functions in involution by Poisson mappings and adding
Casimir functions during the process allows to construct completely integrable
systems. Some examples are investigated in detail.Comment: AmsTeX, 9 page
Un-reduction
This paper provides a full geometric development of a new technique called
un-reduction, for dealing with dynamics and optimal control problems posed on
spaces that are unwieldy for numerical implementation. The technique, which was
originally concieved for an application to image dynamics, uses Lagrangian
reduction by symmetry in reverse. A deeper understanding of un-reduction leads
to new developments in image matching which serve to illustrate the
mathematical power of the technique.Comment: 25 pages, revised versio
On the monotonicity of scalar curvature in classical and quantum information geometry
We study the statistical monotonicity of the scalar curvature for the
alpha-geometries on the simplex of probability vectors. From the results
obtained and from numerical data we are led to some conjectures about quantum
alpha-geometries and Wigner-Yanase-Dyson information. Finally we show that this
last conjecture implies the truth of the Petz conjecture about the monotonicity
of the scalar curvature of the Bogoliubov-Kubo-Mori monotone metric.Comment: 20 pages, 2 .eps figures; (v2) section 2 rewritten, typos correcte
Poisson bracket in classical field theory as a derived bracket
We construct a Leibniz bracket on the space of
all differential forms over the finite-dimensional jet bundle . As
an example, we write Maxwell equations with sources in the covariant
finite-dimensional hamiltonian form.Comment: 4 page
Optimal reparametrizations in the square root velocity framework
The square root velocity framework is a method in shape analysis to define a distance between curves and functional data. Identifying two curves, if the differ by a reparametrization leads to the quotient space of unparametrized curves. In this paper we study analytical and topological aspects of this construction for the class of absolutely continuous curves. We show that the square root velocity transform is a homeomorphism and that the action of the reparametrization semigroup is continuous. We also show that given two -curves, there exist optimal reparametrizations realising the minimal distance between the unparametrized curves represented by them
Tetrad gravity, electroweak geometry and conformal symmetry
A partly original description of gauge fields and electroweak geometry is
proposed. A discussion of the breaking of conformal symmetry and the nature of
the dilaton in the proposed setting indicates that such questions cannot be
definitely answered in the context of electroweak geometry.Comment: 21 pages - accepted by International Journal of Geometric Methods in
Modern Physics - v2: some minor changes, mostly corrections of misprint
Evolution of Quantum Criticality in CeNi_{9-x}Cu_xGe_4
Crystal structure, specific heat, thermal expansion, magnetic susceptibility
and electrical resistivity studies of the heavy fermion system
CeNi_{9-x}Cu_xGe_4 (0 <= x <= 1) reveal a continuous tuning of the ground state
by Ni/Cu substitution from an effectively fourfold degenerate non-magnetic
Kondo ground state of CeNi_9Ge_4 (with pronounced non-Fermi-liquid features)
towards a magnetically ordered, effectively twofold degenerate ground state in
CeNi_8CuGe_4 with T_N = 175 +- 5 mK. Quantum critical behavior, C/T ~ \chi ~
-ln(T), is observed for x about 0.4. Hitherto, CeNi_{9-x}Cu_xGe_4 represents
the first system where a substitution-driven quantum phase transition is
connected not only with changes of the relative strength of Kondo effect and
RKKY interaction, but also with a reduction of the effective crystal field
ground state degeneracy.Comment: 15 pages, 9 figure
- âŠ