Stability of the conjugate index, degenerate conjugate points and the Maslov index in semi-Riemannian geometry
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...
متن کاملStability of the Focal and Geometric Index in Semi-riemannian Geometry via the Maslov Index
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...
متن کاملOn the Distribution of Conjugate Points along Semi-riemannian Geodesics
Helfer in [6] was the first to produce an example of a spacelike Lorentzian geodesic with a continuum of conjugate points. In this paper we show the following result: given an interval [a, b] of IR and any closed subset F of IR contained in ]a, b], then there exists a Lorentzian manifold (M, g) and a spacelike geodesic γ : [a, b] → M such that γ(t) is conjugate to γ(a) along γ iff t ∈ F .
متن کاملOn the Maslov Index of Symplectic Paths That Are Not Transversal to the Maslov Cycle. Semi-riemannian Index Theorems in the Degenerate Case
The Maslov index of a symplectic path, under a certain transversality assumption, is given by an algebraic count of the intersections of the path with a subvariety of the Lagrangian Grassmannian called the Maslov cycle. In these notes we use the notion of generalized signatures at a singularity of a smooth curve of symmetric bilinear forms to determine a formula for the computation of the Maslo...
متن کاملOn the Maslov Index of Lagrangian Paths That Are Not Transversal to the Maslov Cycle. Semi-riemannian Index Theorems in the Degenerate Case
The Maslov index of a Lagrangian path, under a certain transversality assumption, is given by an algebraic count of the intersections of the path with a subvariety of the Lagrangian Grassmannian called the Maslov cycle. In these notes we use the notion of generalized signatures at a singularity of a smooth curve of symmetric bilinear forms to determine a formula for the computation of the Maslo...
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ژورنال
عنوان ژورنال: Pacific Journal of Mathematics
سال: 2002
ISSN: 0030-8730
DOI: 10.2140/pjm.2002.206.375