Homogeneity on three-dimensional contact metric manifolds

DOI10.1007/BF02785585zbMath0957.53017MaRDI QIDQ1969008

Giovanni Calvaruso, Domenico Perrone, Lieven Vanhecke

Publication date: 16 March 2000

Published in: Israel Journal of Mathematics (Search for Journal in Brave)

zbMATH Keywords

Ricci operatorunimodular Lie groupcurvature homogeneousCodazzi tensorcyclic-parallel Ricci tensorball-homogeneous spaceconformally flat contact metric manifold

Mathematics Subject Classification ID

Differential geometry of homogeneous manifolds (53C30) Special Riemannian manifolds (Einstein, Sasakian, etc.) (53C25) Contact manifolds (general theory) (53D10)

Related Items (26)

Taut contact circles and bi-contact metric structures on three-manifolds ⋮ Pseudo-parallel characteristic Jacobi operators on contact metric 3 manifolds ⋮ A class of 3-dimensional contact metric manifolds ⋮ Contact 3-manifolds with pseudo-parallel characteristic Jacobi operator ⋮ A survey of Riemannian contact geometry ⋮ Pseudo-Einstein manifolds ⋮ On the Blair's conjecture for contact metric three-manifolds ⋮ CURVATURE HOMOGENEITY AND BALL-HOMOGENEITY ON ALMOST COKӒHLER 3-MANIFOLDS ⋮ A generalization of \(K\)-contact and \((k, \mu )\)-contact manifolds ⋮ A class of conformally flat contact metric 3-manifolds ⋮ CONFORMALLY FLAT CONTACT THREE-MANIFOLDS ⋮ A study of three-dimensional paracontact (κ̃,μ̃,ν̃)-spaces ⋮ D-homothetic transforms of \(\varphi\)-symmetric spaces ⋮ Pseudo-Hermitian symmetries ⋮ Homogeneity and local symmetry of complex (\(\kappa, \mu)\)-spaces ⋮ Strongly locally \(\varphi \)-symmetric contact metric manifolds ⋮ When is the unit tangent sphere bundle semi-symmetric? ⋮ Conformally flat real hypersurfaces in nonflat complex planes ⋮ CERTAIN RESULTS ON THREE-DIMENSIONAL CONTACT METRIC MANIFOLDS ⋮ Harmonicity of unit vector fields with respect to Riemannian \(g\)-natural metrics ⋮ Harmonic characteristic vector fields on contact metric three-manifolds ⋮ CONTACT METRIC THREE-MANIFOLDS WITH CONSTANT SCALAR TORSION ⋮ Three dimensional contact metric manifolds with Cotton solitons ⋮ Strongly pseudo-convex CR space forms ⋮ Special directions on contact metric three-manifolds ⋮ Torsion and homogeneity on contact metric three-manifolds

Cites Work

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• Symmetries and \(\phi\)-symmetric spaces
• Isometric, holomorphic and symplectic reflections
• Homogeneous contact Riemannian three-manifolds
• Geodesic symmetries in Sasakian locally \(\Phi\)-symmetric spaces
• Ball-homogeneous and disk-homogeneous Riemannian manifolds
• Conformally flat Riemannian manifolds admitting a transitive group of isometries
• Contact manifolds in Riemannian geometry
• Curvatures of left invariant metrics on Lie groups
• Sasakian \(\varphi\)-symmetric spaces
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• On 3-dimensional contact metric manifolds with \(\nabla_\xi\tau=0\)
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