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

DOI10.24033/asens.2487zbMath1497.53120arXiv1510.00275OpenAlexW2237955143WikidataQ123143566 ScholiaQ123143566MaRDI QIDQ5085457

Stefan Rosemann, Vladimir S. Matveev, Alexei V. Bolsinov

Publication date: 27 June 2022

Published in: Annales scientifiques de l'École Normale Supérieure (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1510.00275

zbMATH Keywords

projective transformations Kähler geometry projectively equivalent metrics rigidity results geodesically equivalent metrics Hamiltonian 2-form \(c\)-projective transformations \(c\)-projectively equivalent metrics

Mathematics Subject Classification ID

Global differential geometry of Hermitian and Kählerian manifolds (53C55) Geodesics in global differential geometry (53C22) Rigidity results (53C24) General geometric structures on manifolds (almost complex, almost product structures, etc.) (53C15) Compact Kähler manifolds: generalizations, classification (32J27) Connections (general theory) (53C05) Projective differential geometry (53A20) Affine differential geometry (53A15)

Related Items (8)

Argument shift method and sectional operators: applications to differential geometry ⋮ Metrics admitting projective and c-projective vector fields ⋮ \(J\)-trajectories in 4-dimensional solvable Lie group \(\mathrm{Sol}_1^4\) ⋮ Applications of Nijenhuis geometry. V: Geodesic equivalence and finite-dimensional reductions of integrable quasilinear systems ⋮ Curvature and the c-projective mobility of Kähler metrics with hamiltonian 2-forms ⋮ Projectively invariant objects and the index of the group of affine transformations in the group of projective transformations ⋮ Geodesic rigidity of Levi-Civita connections admitting essential projective vector fields ⋮ Geodesic flows of c-projectively equivalent metrics are quantum integrable

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