We give a necessary and sufficient condition for an n-dimensional Riemannian manifold to be isometrically immersed in Sn×R or Hn×R in terms of its first and second fundamental forms and of the projection of the vertical vector field on its tangent plane. We deduce the existence of a one-parameter family of isometric minimal deformations of a given minimal surface in S2 ×R or H2 × R, obtained by...

We generalize the spinorial characterization of isometric immersions of surfaces in R given by T. Friedrich to surfaces in S and H. The main argument is the interpretation of the energy-momentum tensor associated with a special spinor field as a second fundamental form. It turns out that such a characterization of isometric immersions in terms of a special section of the spinor bundle also hold...

Constrained Willmore surfaces are conformal immersions of Riemann surfaces that are critical points of the Willmore energy W = R H 2 under compactly supported infinitesimal conformal variations. Examples include all constant mean curvature surfaces in space forms. In this paper we investigate more generally the critical points of arbitrary geometric functionals on the space of immersions under ...

In the first part, we give a self contained introduction to the theory of cyclic systems in n-dimensional space which can be considered as immersions into certain Grassmannians. We show how the (metric) geometries on spaces of constant curvature arise as subgeometries of Möbius geometry which provides a slightly new viewpoint. In the second part we characterize Guichard nets which are given by ...

Using Legendrian immersions and, in particular, Legendre curves in odd dimensional spheres and anti De Sitter spaces, we provide a method of construction of new examples of Hamiltonian-minimal Lagrangian submanifolds in complex projective and hyperbolic spaces, including explicit one parameter families of embeddings of quotients of certain product manifolds. In addition, new examples of minimal...

The boundary of a DoCarmo-Wallach moduli space parametrizing (harmonic) eigenmaps between spheres or spherical minimal immersions carries a natural stratification. In this paper we study the critical points of the distance function on the boundary strata. We show that the critical points provide a natural generalization of eigenmaps with L-orthonormal components. We also point out that many cla...

We propose a new adaptive spatio-temporal interpolation method that combines either by a step or a line function existing spatial and temporal interpolation methods. We test the new method using climate data obtained from weather stations in Colorado and Nebraska, for the time period from 1993 to 2003. The experimental results show that in mountainous regions our adaptive spatio-temporal method...

We study the new geometric flow that was introduced in [11] that evolves a pair of map and (domain) metric in such a way that it changes appropriate initial data into branched minimal immersions. In the present paper we focus on the existence theory as well as the issue of uniqueness of solutions. We establish that a (weak) solution exists for as long as the metrics remain in a bounded region o...

This is a companion paper to [1] where we introduced the spinorial energy functional and studied its main properties in dimensions equal or greater than three. In this article we focus on the surface case. A salient feature here is the scale invariance of the functional which leads to a plenitude of critical points. Moreover, via the spinorial Weierstraß representation it relates to the Willmor...