The Morse index theorem in semi-Riemannian geometry

DOI10.1016/S0040-9383(01)00030-1zbMath1040.53052arXivmath/0011090OpenAlexW2101746690WikidataQ115339865 ScholiaQ115339865MaRDI QIDQ1849799

Daniel V. Tausk, Paolo Piccione

Publication date: 2 December 2002

Published in: Topology (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0011090

zbMATH Keywords

geodesicsconjugate pointsMorse indexMaslov indexindefinite metrics

Mathematics Subject Classification ID

Hamilton's equations (70H05) Geodesics in global differential geometry (53C22) Global differential geometry of Lorentz manifolds, manifolds with indefinite metrics (53C50) Lagrangian submanifolds; Maslov index (53D12) Geodesy, mapping problems (86A30) Variational problems in applications to the theory of geodesics (problems in one independent variable) (58E10)

Related Items (15)

Maslov index in semi-Riemannian submersions ⋮ The Maslov index in weak symplectic functional analysis ⋮ The Maslov index and some applications to dispersion relations in curved space times ⋮ Computation of the Maslov index and the spectral flow via partial signatures. ⋮ A 𝐾-theoretic proof of the Morse index theorem in semi-Riemannian geometry ⋮ Yet another proof of the Morse index theorem ⋮ On a formula for the spectral flow and its applications ⋮ The Maslov Index in Symplectic Banach Spaces ⋮ A Morse-Smale index theorem for indefinite elliptic systems and bifurcation ⋮ Morse theory of causal geodesics in a stationary spacetime via Morse theory of geodesics of a Finsler metric ⋮ General spectral flow formula for fixed maximal domain ⋮ A bifurcation result for semi-Riemannian trajectories of the Lorentz force equation ⋮ Spectral flow and iteration of closed semi-Riemannian geodesics ⋮ On the usefulness of an index due to Leray for studying the intersections of Lagrangian and symplectic paths ⋮ On the Morse index of Lagrangian systems.

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