3,501 research outputs found
K\"ahler manifolds with geodesic holomorphic gradients
A vector field on a Riemannian manifold is called geodesic if its integral
curves are reparametrized geodesics. We classify compact K\"ahler manifolds
admitting nontrivial real-holomorphic geodesic gradient vector fields that
satisfy an additional integrability condition. They are all biholomorphic to
bundles of complex projective spaces.Comment: 52 page
Metastable supersymmetry breaking without scales
We construct new examples of models of metastable D=4 N=1 supersymmetry
breaking in which all scales are generated dynamically. Our models rely on
Seiberg duality and on the ISS mechanism of supersymmetry breaking in massive
SQCD. Some of the electric quark superfields arise as composites of a strongly
coupled gauge sector. This allows us to start with a simple cubic
superpotential and an asymptotically free gauge group in the ultraviolet, and
end up with an infrared effective theory which breaks supersymmetry dynamically
in a metastable state.Comment: 6 pages, 1 figure; v2: journal versio
On the manifold structure of the set of unparameterized embeddings with low regularity
Given manifolds and , with compact, we study the geometrical
structure of the space of embeddings of into , having less regularity
than , quotiented by the group of diffeomorphisms of .Comment: To appear in the Bulletin of the Brazilian Mathematical Societ
Infinitely many solutions to the Yamabe problem on noncompact manifolds
We establish the existence of infinitely many complete metrics with constant scalar curvature on prescribed conformal classes on certain noncompact product manifolds. These include products of closed manifolds with constant positive scalar curvature and simply-connected symmetric spaces of noncompact or Euclidean type; in particular, , , , and , . As a consequence, we obtain infinitely many periodic solutions to the singular Yamabe problem on , for all , the maximal range where nonuniqueness is possible. We also show that all Bieberbach groups in are periods of bifurcating branches of solutions to the Yamabe problem on , ,
Spectral flow and iteration of closed semi-Riemannian geodesics
We introduce the notion of spectral flow along a periodic semi-Riemannian
geodesic, as a suitable substitute of the Morse index in the Riemannian case.
We study the growth of the spectral flow along a closed geodesic under
iteration, determining its asymptotic behavior.Comment: LaTeX2e, 21 page
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