106 research outputs found
Weyl-parallel forms, conformal products and Einstein-Weyl manifolds
Motivated by the study of Weyl structures on conformal manifolds admitting
parallel weightless forms, we define the notion of conformal product of
conformal structures and study its basic properties. We obtain a classification
of Weyl manifolds carrying parallel forms, and we use it to investigate the
holonomy of the adapted Weyl connection on conformal products. As an
application we describe a new class of Einstein-Weyl manifolds of dimension 4.Comment: 24 page
On the irreducibility of locally metric connections
A locally metric connection on a smooth manifold is a torsion-free
connection on with compact restricted holonomy group
. If the holonomy representation of such a connection is
irreducible, then preserves a conformal structure on . Under some
natural geometric assumption on the life-time of incomplete geodesics, we prove
that conversely, a locally metric connection preserving a conformal
structure on a compact manifold has irreducible holonomy representation,
unless or is the Levi-Civita connection of a
Riemannian metric on . This result generalizes Gallot's theorem on the
irreducibility of Riemannian cones to a much wider class of connections. As an
application, we give the geometric description of compact conformal manifolds
carrying a tame closed Weyl connection with non-generic holonomy.Comment: 26 pages, 4 figure
Symmetries of Contact Metric Manifolds
We study the Lie algebra of infinitesimal isometries on compact Sasakian and
K--contact manifolds. On a Sasakian manifold which is not a space form or
3--Sasakian, every Killing vector field is an infinitesimal automorphism of the
Sasakian structure. For a manifold with K--contact structure, we prove that
there exists a Killing vector field of constant length which is not an
infinitesimal automorphism of the structure if and only if the manifold is
obtained from the Konishi bundle of a compact pseudo--Riemannian
quaternion--Kaehler manifold after changing the sign of the metric on a maximal
negative distribution. We also prove that non--regular Sasakian manifolds are
not homogeneous and construct examples with cohomogeneity one. Using these
results we obtain in the last section the classification of all homogeneous
Sasakian manifolds.Comment: 14 pages, LaTeX2e, some comments and references adde
- …