Let f:Σ→Q3 be the space form projection of a Legendre map f:Σ→Z into the (Riemannian or Lorentzian) space form Q3 with constant sectional curvature κ. Let ε be +1 in the case that Q3 is a Riemannian space form and −1 in the case that it is Lorentzia…

Using the gauge theoretic approach for Lie applicable surfaces, we characterise certain subclasses of surfaces in terms of polynomial conserved quant…

Invariant notions of a class of Segre varieties $\Segrem(2)$ of PG(2^m - 1, 2) that are direct products of $m$ copies of PG(1, 2), $m$ being any posi…

It is well-known that there exist bar-joint frameworks (without continuous flexions) whose physical models can snap between different realizations du…

The class of linear pentapods with a simple singularity variety is obtained by imposing architectural restrictions on the design in such a way that t…

It is well-known that there exists a bijection between the set of lines of the projective 3-dimensional space $P^3$ and all real points of the so-cal…

Dirac-harmonic maps with curvature term arise as critical points of part of the supersymmetric nonlinear σ-model from quantum field theory [15], p. 268. They form a pair of a map from a Riemann spin manifold to another Riemannian manifold coupled wi…

We study the qualitative behavior of nonlinear Dirac equations arising in quantum field theory on complete Riemannian manifolds. In particular, we de…

In this section we derive a Liouville theorem for harmonic maps with potential from complete noncompact manifolds with positive Ricci curvature. Our result is motivated from a similar result for harmonic maps, see [18, Theorem 1]. In addition, this …

In this note we discuss how several results characterizing the qualitative behavior of solutions to the nonlinear Poisson equation can be generalized…

The given kinematic interpretation of all points of the Study quadric’s ambient space P7 in terms of X4-displacements can e.g. be used for the interactive design of rational motions in the following way (see Fig. 2):

It is well known that real points of the Study quadric (sliced along a 3-dimensional generator space) correspond to displacements of the Euclidean 3-…

Let $S_{(N)} \equiv PG(1,\,2) \times PG(1,\,2) \times \cdots \times PG(1,\,2)$ be a Segre variety that is $N$-fold direct product of projective lines…

As we have seen in the introduction the full (1,1) non-linear supersymmetric sigma model studied in quantum field theory involves an additional curvature term in the energy functional, namely

We study Dirac-harmonic maps from surfaces to manifolds with torsion, which is motivated from the superstring action considered in theoretical physic…

A linear pentapod is a parallel manipulator with five collinear anchor points on the motion platform (end-effector), which are connected via extendib…

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