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6 papers · 1 filter
Properties and Transformations of Weingarten Surfaces
Brendan Guilfoyle, Morgan Robson
The Weingarten relations satisfied by rotationally symmetric surfaces in Euclidean 3-space E3 are considered from three points of view: restrictions on the slope of the relation at…
On the Convergence of Non-Integer Linear Hopf Flow
Brendan Guilfoyle, Morgan Robson
The evolution of a rotationally symmetric surface by a linear combination of its radii of curvature equation is considered. It is known that if the coefficients form certain intege…
Almost Paracomplex Structures on 4-Manifolds
Nikos Georgiou, Brendan Guilfoyle
Reflection in a line in Euclidean 3-space defines an almost paracomplex structure on the space of all oriented lines, isometric with respect to the canonical neutral Kaehler metric…
A new geometric structure on tangent bundles
Nikos Georgiou, Brendan Guilfoyle
For a Riemannian manifold , we construct a scalar flat metric in the tangent bundle . It is locally conformally flat if and only if either, is a 2-dimensional ma…
Hopf hypersurfaces in spaces of oriented geodesics
Nikos Georgiou, Brendan Guilfoyle
A Hopf hypersurface in a (para-)Kaehler manifold is a real hypersurface for which one of the principal directions of the second fundamental form is the (para-)complex dual of the n…
On Hamiltonian minimal submanifolds in the space of oriented geodesics in real space forms
Nikos Georgiou, Guillermo Antonio Lobos Villagra
We prove that a deformation of a hypersurface in a -dimensional real space form induce a Hamiltonian variation of the normal congruence in the spac…