Gauss maps of harmonic and minimal great circle fibrations

DOI10.1007/s10455-023-09886-0OpenAlexW4320556457WikidataQ126053249 ScholiaQ126053249MaRDI QIDQ2684459

Andreas Savas-Halilaj, Michael Markellos, Ioannis Fourtzis

Publication date: 16 February 2023

Published in: Annals of Global Analysis and Geometry (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2203.12404

zbMATH Keywords

maximum principleGauss mapsHopf vector fieldsgreat circle fibration

Mathematics Subject Classification ID

Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) (53C42) Global submanifolds (53C40) Differential geometric aspects of harmonic maps (53C43) Harmonic maps, etc. (58E20) Rigidity results (53C24) Other geometric structures on 3-manifolds (57K35)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• On deformable minimal hypersurfaces in space forms
• On the differential geometry of tangent bundles of Riemannian manifolds
• Great circle fibrations of the three-sphere
• On the volume of a unit vector field on the three-sphere
• Riemannian submersions with totally geodesic fibers
• Minimal graphs
• Unit vector fields on spheres, which are harmonic maps
• Total bending of flows with mean curvature correction
• Harmonic and minimal vector fields on tangent and unit tangent bundles
• Minimal unit vector fields
• The geometry of the Hopf fibrations
• Total bending of vector fields on Riemannian manifolds
• Complete minimal submanifolds with nullity in Euclidean spheres
• Rigidity of the Hopf fibration
• Great circle fibrations and contact structures on the 3-sphere
• Graphical mean curvature flow with bounded bi-Ricci curvature
• Volume minimising unit vector fields on three dimensional space forms of positive curvature
• Evolution of contractions by mean curvature flow
• Minimal surfaces in \(\mathbb{S}^{2} \times \mathbb{S}^{2}\)
• A critical radius for unit Hopf vector fields on spheres
• Bernstein theorems for length and area decreasing minimal maps
• Conformal Fibrations of $S^3$ by Circles
• On the Geometry of the Tangent Bundle.
• Smooth Great Circle Fibrations and an Application to the Topological Blaschke Conjecture
• Volumes of Vector Fields on Spheres
• Volumes of Flows
• S¹ -Invariant Harmonic Maps From S³ To S²
• The Blaschke conjecture and great circle fibrations of spheres
• The Tension Field of the Gauss Map
• Volume, energy and generalized energy of unit vector fields on Berger spheres: stability of Hopf vector fields
• On the energy of a unit vector field
• Riemannian geometry of contact and symplectic manifolds
• Second variation of volume and energy of vector fields. Stability of Hopf vector fields
• Volume-preserving great circle flows on the 3-sphere

This page was built for publication: Gauss maps of harmonic and minimal great circle fibrations