30 research outputs found
Weyl-Schouten Theorem for symmetric spaces
Let N be a symmetric space of dimension n > 5 whose de Rham decomposition
contains no factors of constant curvature and let W be the Weyl tensor of N at
some point. We prove that a Riemannian manifold whose Weyl tensor at every
point is a positive multiple of W is conformally equivalent to N (the case N =
R^n is the Weyl-Schouten Theorem).Comment: Changed some proofs; corrected typo
Annular and pants thrackles
A thrackle is a drawing of a graph in which each pair of edges meets
precisely once. Conway's Thrackle Conjecture asserts that a thrackle drawing of
a graph on the plane cannot have more edges than vertices. We prove the
Conjecture for thrackle drawings all of whose vertices lie on the boundaries of
connected domains in the complement of the drawing. We also give a
detailed description of thrackle drawings corresponding to the cases when
(annular thrackles) and (pants thrackles).Comment: 17 page
A counterexample to Belgun-Moroianu conjecture
We construct an example of a closed manifold with a nonflat reducible locally
metric connection such that it preserves a conformal structure and such that it
is not the Levi-Civita connection of a Riemannian metric.Comment: are as always welcom
A sufficient condition for a pair of sequences to be bipartite graphic
We present a sufficient condition for a pair of finite integer sequences to
be degree sequences of a bipartite graph, based only on the lengths of the
sequences and their largest and smallest elements.Comment: 5 page