23,807 research outputs found
Equifocality of a singular riemannian foliation
A singular foliation on a complete riemannian manifold M is said to be
riemannian if each geodesic that is perpendicular at one point to a leaf
remains perpendicular to every leaf it meets. We prove that the regular leaves
are equifocal, i.e., the end point map of a normal foliated vector field has
constant rank. This implies that we can reconstruct the singular foliation by
taking all parallel submanifolds of a regular leaf with trivial holonomy. In
addition, the end point map of a normal foliated vector field on a leaf with
trivial holonomy is a covering map. These results generalize previous results
of the authors on singular riemannian foliations with sections.Comment: 10 pages. This version contains some misprints corrections and
improvements of Corollary 1.
Vector bundles on projective varieties and representations of quivers
We present equivalences between certain categories of vector bundles on
projective varieties, namely cokernel bundles, Steiner bundles, syzygy bundles,
and monads, and full subcategories of representations of certain quivers. As an
application, we provide decomposability criteria for such bundles.Comment: 29 pages. Partially overlaps with arXiv:1210.7835. To appear in
Algebra and Discrete Mathematic
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