Stability of Left-Invariant Totally Geodesic Unit Vector Fields on Three-Dimensional Lie Groups

DOI10.1007/978-3-319-04675-4_8zbMath1323.53057arXivmath/0512478OpenAlexW2144938674MaRDI QIDQ5263636

Alexander Yampolsky

Publication date: 17 July 2015

Published in: Springer Proceedings in Mathematics & Statistics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0512478

zbMATH Keywords

variations of volumestable/unstable unit vector fields

Mathematics Subject Classification ID

Differential geometry of homogeneous manifolds (53C30) Global submanifolds (53C40) Methods of local Riemannian geometry (53B21)

Cites Work

• The sectional curvature of the Sasaki metric of \(T_ 1M^ n\)
• On the volume of a unit vector field on the three-sphere
• Curvatures of left invariant metrics on Lie groups
• Relationship between volume and energy of vector fields.
• Harmonic and minimal vector fields on tangent and unit tangent bundles
• Examples of minimal unit vector fields
• Minimal unit vector fields
• Energy and volume of unit vector fields on three-dimensional Riemannian manifolds.
• A totally geodesic property of Hopf vector fields
• Minimal varieties in Riemannian manifolds
• On the Geometry of the Tangent Bundle.
• Unit Tangent Sphere Bundles with Constant Scalar Curvature
• Riemannian geometry of fibre bundles
• Invariant minimal unit vector fields on Lie groups
• Second variation of volume and energy of vector fields. Stability of Hopf vector fields
• Harmonic and minimal radial vector fields
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: Stability of Left-Invariant Totally Geodesic Unit Vector Fields on Three-Dimensional Lie Groups