Conjugate points and Maslov index in locally symmetric semi-Riemannian manifolds
نویسندگان
چکیده
منابع مشابه
Stability of the Conjugate Index, Degenerate Conjugate Points and the Maslov Index in Semi-riemannian Geometry
We investigate the problem of the stability of the number of conjugate or focal points (counted with multiplicity) along a semi-Riemannian geodesic γ. For a Riemannian or a nonspacelike Lorentzian geodesic, such number is equal to the intersection number (Maslov index) of a continuous curve with a subvariety of codimension one of the Lagrangian Grassmannian of a symplectic space. In the general...
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We investigate the problem of the stability of the number of conjugate or focal points (counted with multiplicity) along a semi-Riemannian geodesic γ. For a Riemannian or a non spacelike Lorentzian geodesic, such number is equal to the intersection number (Maslov index) of a continuous curve with a subvariety of codimension one of the Lagrangian Grassmannian of a symplectic space. Such intersec...
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Let M be a Lagrangian manifold, let the 1-form pdx be globally exact on M and let S(x, p) be defined by dS = pdx on M. Let H(x, p) be convex in p for all x and vanish on M . Let V (x) = inf{S(x, p) : p such that (x, p) ∈ M}. Recent work in the literature has shown that (i) V is a viscosity solution of H(x, ∂V/∂x) = 0 provided V is locally Lipschitz, and (ii) V is locally Lipschitz outside the s...
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ژورنال
عنوان ژورنال: Differential Geometry and its Applications
سال: 2006
ISSN: 0926-2245
DOI: 10.1016/j.difgeo.2006.02.007