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An interesting class of axially symmetric surfaces, which generalizes Delaunay's unduloids and provides solutions of the shape equation is described in explicit parametric form. This class provide the first analytical examples of surfaces with periodic curvatures studied by K. Kenmotsu and leads to some unexpected relationships among Jacobian elliptic functions and their integrals.
This is a review article on the motion of charged particles related to the author's study. The equation of motion of a charged particle is defined as a curve satisfying a certain differential equation of second order in a semi-Riemannian manifold furnished with a closed two-form. Charged particle is a generalization of geodesic. We shall oversee the geometric aspect of charged particles.
In this paper we study the second mean curvature for different hypersurfaces in space forms. We furnish some examples and we remind some connections between $II$-minimality and biharmonicity. The main result consists in proving that there are no $II$-minimal translation surfaces in the Euclidean three-space.
This is an introductory paper that provides a first introduction to geometric structures on $TM\oplus T^*M$. It contains definitions and characteristic properties (some of them new) of generalized complex, Kähler, almost contact (normal, contact) and Sasakian manifolds.