Harmonic characteristic vector fields on contact metric three-manifolds

DOI10.1017/S0004972700033773zbMath1034.53050OpenAlexW2159210798MaRDI QIDQ4709802

Domenico Perrone

Publication date: 2003

Published in: Bulletin of the Australian Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1017/s0004972700033773

zbMATH Keywords

curvature tensorharmonic mapsReeb vector fieldunit tangent bundlecontact metric structures

Mathematics Subject Classification ID

Special Riemannian manifolds (Einstein, Sasakian, etc.) (53C25) Differential geometric aspects of harmonic maps (53C43) Contact manifolds (general theory) (53D10)

Related Items (23)

Ricci collineations on 3-dimensional paracontact metric manifolds ⋮ Contact metric manifolds whose characteristic vector field is a harmonic vector field ⋮ Some geometrical properties of the Oscillator group ⋮ Stability of the Reeb vector field of \(H\)-contact manifolds ⋮ A class of 3-dimensional contact metric manifolds ⋮ Harmonic almost contact structures ⋮ \(H\)-contact semi-Riemannian manifolds ⋮ The harmonicity of the Reeb vector field with respect to Riemannian \(g\)-natural metrics ⋮ A study of three-dimensional paracontact (κ̃,μ̃,ν̃)-spaces ⋮ Unit vector fields of minimum energy on quotients of spheres and stability of the Reeb vector field ⋮ Bending and stretching unit vector fields in Euclidean and hyperbolic 3-space ⋮ Some geometrical properties of Berger Spheres ⋮ Almost contact metric manifolds whose Reeb vector field is a harmonic section ⋮ \(H\)-contact unit tangent sphere bundles ⋮ HOMOGENEOUS AND H-CONTACT UNIT TANGENT SPHERE BUNDLES ⋮ On the energy of a unit vector field ⋮ Pseudoharmonic maps and vector fields on \(CR\) manifolds ⋮ Contact pseudo-metric manifolds ⋮ On the geometry of tangent hyperquadric bundles: CR and pseudoharmonic vector fields ⋮ CERTAIN RESULTS ON THREE-DIMENSIONAL CONTACT METRIC MANIFOLDS ⋮ Harmonicity of unit vector fields with respect to Riemannian \(g\)-natural metrics ⋮ Contact semi-Riemannian structures in CR geometry: some aspects ⋮ Harmonic geometric structures: the general theory and the cases of almost complex and almost contact structures

Cites Work

• Unnamed Item
• Curvatures of left invariant metrics on Lie groups
• Unit vector fields on spheres, which are harmonic maps
• Normal contact structures on 3-manifolds
• Relationship between volume and energy of vector fields.
• Examples of minimal unit vector fields
• Minimal and harmonic characteristic vector fields on three-dimensional contact metric manifolds
• Contact metric manifolds satisfying a nullity condition
• Total bending of vector fields on Riemannian manifolds
• Homogeneity on three-dimensional contact metric manifolds
• On the Existence of a New Class of Contact Metric Manifolds
• On the energy of a unit vector field

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