28,012 research outputs found
Isoparameteric hypersurfaces in a Randers sphere of constant flag curvature
In this paper, I study the isoparametric hypersurfaces in a Randers sphere
of constant flag curvature, with the navigation datum . I
prove that an isoparametric hypersurface for the standard round sphere
which is tangent to remains isoparametric for after the
navigation process. This observation provides a special class of isoparametric
hypersurfaces in , which can be equivalently described as the regular
level sets of isoparametric functions satisfying is transnormal. I
provide a classification for these special isoparametric hypersurfaces ,
together with their ambient metric on , except the case that is of
the OT-FKM type with the multiplicities . I also give a
complete classificatoin for all homogeneous hypersurfaces in . They
all belong to these special isoparametric hypersurfaces. Because of the extra
, the number of distinct principal curvature can only be 1,2 or 4, i.e.
there are less homogeneous hypersurfaces for than those for
.Comment: The newest version adds a referenc
Examples of flag-wise positively curved spaces
A Finsler space is called flag-wise positively curved, if for any
and any tangent plane , we can find a nonzero
vector , such that the flag curvature . Though compact positively curved spaces are very rare in both
Riemannian and Finsler geometry, flag-wise positively curved metrics should be
easy to be found. A generic Finslerian perturbation for a non-negatively curved
homogeneous metric may have a big chance to produce flag-wise positively curved
metrics. This observation leads our discovery of these metrics on many compact
manifolds. First we prove any Lie group such that its Lie algebra
is compact non-Abelian and admits flag-wise positively curved left invariant Finsler metrics. Similar
techniques can be applied to our exploration for more general compact coset
spaces. We will prove, whenever is a compact simply connected coset
space, and admit flag-wise positively curved Finsler
metrics. This provides abundant examples for this type of metrics, which are
not homogeneous in general.Comment: 9 pages. In the newest version, Theorem 1.3 is strenghened to provide
many more example
The number of geometrically distinct reversible closed geodesics on a Finsler sphere with
In this paper we study the Finsler sphere with , which has
constant flag curvature and only finite prime closed geodesics. In
this case, the connected isometry group must be a torus which
dimension satisfies . We will prove that
the number of geometrically distinct reversible closed geodesics on
is at least . When , the
equality happens, and there are exactly prime closed
geodesics, which verifies Anosov conjecture in this special case
Homogeneous Finsler spaces with only one orbit of prime closed geodesics
When a closed Finsler manifold admits continuous isometric actions,
estimating the number of orbits of prime closed geodesics seems a more
reasonable substitution for estimating the number of prime closed geodesics. To
generalize the works of H. Duan, Y. Long, H.B. Rademacher, W. Wang and others
on the existence of two prime closed geodesics to the equivariant situation, we
purpose the question if a closed Finsler manifold has only one orbit of prime
closed geodesic if and only if it is a compact rank-one Riemannian symmetric
space. In this paper, we study this problem in homogeneous Finsler geometry,
and get a positive answer when the dimension is even or the metric is
reversible. We guess the rank inequality and algebraic techniques in this paper
may continue to play an important role for discussing our question in the
non-homogeneous situation.Comment: 29 page
Geodesic orbit spheres and constant curvature in Finsler geometry
In this paper, we generalize the classification of geodesic orbit spheres
from Riemannian geometry to Finsler geometry. Then we further prove if a
geodesic orbit Finsler sphere has constant flag curvature, it must be Randers.
It provides an alternative proof for the classification of invariant Finsler
metrics with on homogeneous spheres other than .Comment: In version 2 of this paper, a reference has been added, and a minor
mistake in the introduction section has been correcte
Maxwell's equal area law for Lovelock Thermodynamics
We present the construction of Maxwell's equal area law for the Guass-Bonnet
AdS black holes in and third order Lovelock AdS black holes in .
The equal area law can be used to find the number and location of the points of
intersection in the plots of Gibbs free energy, so that we can get the
thermodynamically preferred solution which corresponds to the first order phase
transition. We obtain the radius of the small and large black holes in the
phase transition which share the same Gibbs free energy. The case with two
critical points is explored in much more details. The latent heat is also
studied.Comment: 16 pages, 10 figures. V2: minor corrections and new references. V3:
more discussion about the relationship between latent heat and temperature
added. Accepted by IJMP
Early thermalization of quark-gluon matter by elastic 3-to-3 scattering
The early thermalization is crucial to the quark-gluon plasma as a perfect
liquid and results from many-body scattering. We calculate squared amplitudes
for elastic parton-parton-parton scattering in perturbative QCD. Transport
equations with the squared amplitudes are established and solved to obtain the
thermalization time of initially produced quark-gluon matter and the initial
temperature of quark-gluon plasma. We find that the thermalization times of
quark matter and gluon matter are different.Comment: 5 pages, 1 figure, proceedings for Extreme QCD 201
Early Thermalization at RHIC
Triple-gluon elastic scatterings are briefly reviewed since the scatterings
explain the early thermalization puzzle in Au-Au collisions at RHIC energies. A
numerical solution of the transport equation with the triple-gluon elastic
scatterings demonstrates gluon momentum isotropy achieved at a time of the
order of 0.65 fm/c. Triple-gluon scatterings lead to a short thermalization
time of gluon matter.Comment: LaTex, 8 pages and 4 figures, talk presented in the Weihai workshop
on relativistic heavy ion collision
On Bondage Numbers of Graphs -- a survey with some comments
The bondage number of a nonempty graph is the cardinality of a smallest
edge set whose removal from results in a graph with domination number
greater than the domination number of . This lecture gives a survey on the
bondage number, including the known results, problems and conjectures. We also
summarize other types of bondage numbers.Comment: 80 page; 14 figures; 120 reference
Origin of Temperature of Quark-Gluon Plasma in Heavy Ion Collisions
Initially produced quark-gluon matter at RHIC and LHC does not have a
temperature. A quark-gluon plasma has a high temperature. From this quark-gluon
matter to the quark-gluon plasma is the early thermalization or the rapid
creation of temperature. Elastic three-parton scattering plays a key role in
the process. The temperature originates from the two-parton scattering, the
three-parton scattering, the four-parton scattering and so forth in quark-gluon
matter.Comment: 6 pages, proceedings for the XXX-th International Workshop on High
Energy Physic
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