1. CMB 2016 (vol 59 pp. 575)
||Cohomogeneity One Randers Metrics|
An action of a Lie group $G$ on a smooth manifold $M$ is called
cohomogeneity one if the orbit space $M/G$ is of dimension $1$.
A Finsler metric $F$ on $M$ is called invariant if $F$ is
invariant under the action of $G$. In this paper,
we study invariant
Randers metrics on cohomogeneity one manifolds. We first give a
sufficient and necessary condition for the existence of invariant
Randers metrics on cohomogeneity one manifolds. Then we obtain
some results on invariant Killing vector fields on the
cohomogeneity one manifolds and use that to deduce some
sufficient and necessary condition for a cohomogeneity one
Randers metric to be Einstein.
Keywords:cohomogeneity one actions, normal geodesics, invariant vector fields, Randers metrics
2. CMB 2010 (vol 53 pp. 412)
||Einstein-Like Lorentz Metrics and Three-Dimensional Curvature Homogeneity of Order One|
We completely classify three-dimensional Lorentz manifolds, curvature homogeneous up to order one, equipped with Einstein-like metrics. New examples arise with respect to both homogeneous examples and three-dimensional Lorentz manifolds admitting a degenerate parallel null line field.
Keywords:Lorentz manifolds, curvature homogeneity, Einstein-like metrics
Categories:53C50, 53C20, 53C30
3. CMB 1997 (vol 40 pp. 204)
||The $\eta$-invariants of cusped hyperbolic $3$-manifolds |
In this paper, we define the $\eta$-invariant for a cusped hyperbolic
$3$-manifold and discuss some of its applications. Such an
invariant detects the chirality of a hyperbolic knot or link and
can be used to distinguish many links with homeomorphic complements.
Categories:57M50, 53C30, 58G25