Metrics admitting projective and c-projective vector fields

DOI10.1090/conm/788/15827zbMath1523.53017OpenAlexW4387319641MaRDI QIDQ6073424

Jan Schumm, Gianni Manno, Andreas Vollmer

Publication date: 15 September 2023

Published in: The Diverse World of PDEs (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/conm/788/15827

zbMATH Keywords

projective vector fieldsc-projective vector fieldsLie problems

Mathematics Subject Classification ID

Local Riemannian geometry (53B20) Projective differential geometry (53A20) Projective connections (53B10)

Cites Work

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• Two-dimensional metrics admitting precisely one projective vector field
• Metrisability of three-dimensional path geometries
• Geodesically equivalent metrics in general relativity
• Proof of the projective Lichnerowicz-Obata conjecture
• Proof of the projective Lichnerowicz conjecture for pseudo-Riemannian metrics with degree of mobility greater than two
• Normal forms for pseudo-Riemannian 2-dimensional metrics whose geodesic flows admit integrals quadratic in momenta
• Riemannian manifolds admitting a projective vector field
• Finding collineations of Kimura metrics
• Holomorphically projective mappings and their generalizations
• Projective transformations of pseudo-Riemannian manifolds
• Geodesic equivalence via integrability
• The Obata conjecture for dimension 2
• Proof of the Yano-Obata conjecture for \(h\)-projective transformations
• 3-dimensional Levi-Civita metrics with projective vector fields
• Four-dimensional Kähler metrics admitting c-projective vector fields
• Metrisability of two-dimensional projective structures
• Normal forms of two-dimensional metrics admitting exactly one essential projective vector field
• Geodesic rigidity of Levi-Civita connections admitting essential projective vector fields
• (Super-)integrable systems associated to 2-dimensional projective connections with one projective symmetry
• Conification construction for Kähler manifolds and its application in \(c\)-projective geometry
• Lichnerowicz-Obata conjecture in dimension two
• A solution of a problem of Sophus Lie: normal forms of two-dimensional metrics admitting two projective vector fields
• Hamiltonian 2-forms in Kähler geometry. II: Global classification
• The only Kähler manifold with degree of mobility at least 3 is (ℂP (n ), _{ɡ Fubini-Study} )
• Splitting and gluing lemmas for geodesically equivalent pseudo-Riemannian metrics
• On Liouville integrability of $h$-projectively equivalent Kähler metrics
• C-projective geometry
• Local normal forms for c-projectively equivalent metrics and proof of the Yano-Obata conjecture in arbitrary signature. Proof of the projective Lichnerowicz conjecture for Lorentzian metrics
• Local normal forms for geodesically equivalent pseudo-Riemannian metrics
• Metric connections in projective differential geometry
• Curvature in Hermitian metric

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