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Compact Riemannian Manifolds with Homogeneous Geodesics
A homogeneous Riemannian space is called a geodesic orbit space
(shortly, GO-space) if any geodesic is an orbit of one-parameter subgroup of
the isometry group . We study the structure of compact GO-spaces and give
some sufficient conditions for existence and non-existence of an invariant
metric with homogeneous geodesics on a homogeneous space of a compact Lie
group . We give a classification of compact simply connected GO-spaces of positive Euler characteristic. If the group is simple and the
metric does not come from a bi-invariant metric of , then is one of
the flag manifolds or and
is any invariant metric on which depends on two real parameters. In
both cases, there exists unique (up to a scaling) symmetric metric such
that is the symmetric space or, respectively,
. The manifolds , are weakly symmetric spaces
Kinetic equations for ultrarelativistic particles in a Robertson-Walker Universe and isotropization of relict radiation by gravitational interactions
Kinetic equations for ultrarelativistic particles with due account of
gravitational interactions with massive particles in the Robertson-Walker
universe are obtained. On the basis of an exact solution of the kinetic
equations thus obtained, a conclusion is made as to the high degree of the
uniformity of the relict radiation on scales with are less than .Comment: 19 pages, 2 figures, 13 reference
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