A note on the Morse index theorem for geodesics between submanifolds in semi-Riemannian geometry

DOI10.1063/1.533113zbMath0982.53037arXivmath/9905136OpenAlexW1982024735WikidataQ115328205 ScholiaQ115328205MaRDI QIDQ4498500

Daniel V. Tausk, Paolo Piccione

Publication date: 16 August 2000

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/9905136

zbMATH Keywords

geodesicsLorentzian manifoldtimelike geodesicsMorse index theoremfocal index theorem

Mathematics Subject Classification ID

Abstract critical point theory (Morse theory, Lyusternik-Shnirel'man theory, etc.) in infinite-dimensional spaces (58E05) Geodesics in global differential geometry (53C22) Global differential geometry of Lorentz manifolds, manifolds with indefinite metrics (53C50) Global Riemannian geometry, including pinching (53C20)

Related Items (7)

Functions on the sphere with critical points in pairs and orthogonal geodesic chords ⋮ Maslov index in semi-Riemannian submersions ⋮ The Maslov index and some applications to dispersion relations in curved space times ⋮ The Morse index theorem in the case of two variable endpoints in conic Finsler manifolds ⋮ A finite dimensional approach to light rays in general relativity ⋮ Pseudo Focal Points Along Lorentzian Geodesics and Morse Index ⋮ Nonisolated spacelike focal and conjugate points in Lorentzian geometry

Cites Work

• Unnamed Item
• The index theorem in Riemannian geometry
• An intrinsic approach to the geodesical connectedness of stationary Lorentzian manifolds
• A focal index theorem for null geodesics
• A Morse index theorem for null geodesics
• Some properties of the spectral flow in semi-Riemannian geometry
• Conjugate points on spacelike geodesics or pseudo-self-adjoint Morse-Sturm-Liouville systems
• A generalized Sturm theorem
• Correction to 'The index theorem in Riemannian geometry', by W. Ambrose

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