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Maslov index in semi-Riemannian submersions. (English) Zbl 1201.53078
The central issue in this article is to study the Maslov index of a horizontal geodesic. More exactly, the focal points and the Maslov index are studied of a horizontal geodesic \( \nu : I \rightarrow M\) in the total space of a semi-Riemannian submersion \(\pi : M \rightarrow B\) by determining an explicit relation with the corresponding objects along the projective geodesic \(\pi\circ \nu : I \rightarrow B\) in the base space. Also it is proved an invariance property of the Maslov index of a semi-Riemannian geodesic by arbitrary changes of trivialization of the tangent bundle along the geodesic.

53C50 Global differential geometry of Lorentz manifolds, manifolds with indefinite metrics
53D12 Lagrangian submanifolds; Maslov index
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