Remark on surfaces with locally spherical indicatrix of normal curvature in a $5$-dimensional space

A remark on capillary surfaces in a 3-dimensional space of constant curvature

We generalize a theorem by J. Choe on capillary surfaces for arbitrary 3-dimensional spaces of constant curvature. The main tools in this paper are an extension of a theorem of H. Hopf due to S.-S. Chern and two index lemmas by J. Choe.

Hypersurfaces with Constant Mean Curvature in a Lorentzian Space Form

Surfaces of constant curvature in 3-dimensional space forms

The study of surfaces immersed in a 3-dimensional ambient space plays a central role in the theory of submanifolds. In addition, Riemannian manifolds with constant sectional curvature can be considered as the most simple examples. Thus, one can think of surfaces with constant Gauss curvature in the Euclidean space R, hyperbolic space H or 3-sphere S as very natural objects of study. Through the...

On locally spherical polytopes of type {5, 3, 5}

There are only finitely many locally projective regular polytopes of type {5, 3, 5}. They are covered by a locally spherical polytope whose automorphism group is J1 × J1 × L2(19), where J1 is the first Janko group, of order 175560, and L2(19) is the projective special linear group of order 3420. This polytope is minimal, in the sense that any other polytope that covers all locally projective po...

Two-dimensional Crystallisation on Spherical Surfaces

We report results of a computational study on 2D crystallisation for a 25-particle Lennard-Jones system on a spherical surface, as a function of radius. The energy is minimised using simulated annealing and steepest descent methods. Different crystalline arrangements with clear energy minima are found at different radii. Qualitatively, most of the observed phenomena are representative also for ...