Hyperkähler metrics of cohomogeneity one

DOI10.1016/S0393-0440(96)00017-4zbMath0909.53032MaRDI QIDQ677516

Andrew S. Dancer, Andrew F. Swann

Publication date: 25 March 1999

Published in: Journal of Geometry and Physics (Search for Journal in Brave)

zbMATH Keywords

hyper-Kähler metricsEinstein equationsCalabi metriccohomogeneity one metrics

Mathematics Subject Classification ID

Groups acting on specific manifolds (57S25) Special Riemannian manifolds (Einstein, Sasakian, etc.) (53C25) Lie algebras of Lie groups (22E60)

Related Items (16)

Auxiliary field methods in supersymmetric nonlinear sigma models ⋮ Hyper-Kähler sigma models on (co)tangent bundles with \(\text{SO}(n)\) isometry ⋮ Unnamed Item ⋮ SU(3)-manifolds of cohomogeneity one ⋮ QUATERNIONIC KAHLER MANIFOLDS OF COHOMOGENEITY ONE ⋮ C-projective symmetries of submanifolds in quaternionic geometry ⋮ Invariant forms, associated bundles and Calabi-Yau metrics ⋮ Calabi-Yau manifolds of cohomogeneity one as complex line bundles ⋮ Calibrated subbundles in noncompact manifolds of special holonomy ⋮ Hyper-Kähler Calabi metrics, \(L^2\) harmonic forms, resolved M2-branes, and AdS\(_4\)/CFT\(_3\) correspondence ⋮ \(SO\) and \(USp\) Kähler and hyper-Kähler quotients and lumps ⋮ Spacetime singularity resolution by M-theory fivebranes: Calibrated geometry, anti-de Sitter solutions and special holonomy metrics ⋮ Cohomogeneity-three hyper-Kähler metrics on nilpotent orbits ⋮ Harmonic forms and deformation of ALC metrics with Spin(7) holonomy ⋮ On spin(7) holonomy metric based on \(\text{SU}(3)/\text{U}(1)\). I ⋮ On spin(7) holonomy metric based on \(\text{SU}(3)/\text{U}(1). \) II

Cites Work

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• HyperKähler and quaternionic Kähler geometry
• Variétés de Jacobi et espaces homogènes de contact complexes. (Manifolds with Jacobi structure and complex contact homogeneous spaces)
• The initial value problem for cohomogeneity one Einstein metrics
• The splitting theorem for manifolds of nonnegative Ricci curvature
• Quaternion Riemann spaces with transitive reductive or solvable groups of motions
• Métriques kählériennes et fibrés holomorphes
• Algebraic constructions of integrable dynamical systems-extensions of the Volterra system
• Kähler–Einstein metrics with SU(2) action
• Introduction to Lie Algebras and Representation Theory

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