Related papers: Isothermic hypersurfaces in R^{n+1}
Universal thermal data in conformal field theory (CFT) offer a valuable means for characterizing and classifying criticality. With improved tensor network techniques, we investigate the universal thermodynamics on a nonorientable minimal…
We prove integral formulas for closed hypersurfaces in C^{n+1}, which furnish a relation between elementary symmetric functions in the eigenvalues of the complex Hessian matrix of the defining function and the Levi curvatures of the…
We study the Bonnet problem for surfaces in 4-dimensional space forms, where two isometric surfaces have the same mean curvature if there exists a parallel vector bundle isometry between their normal bundles that preserves the mean…
In this paper we present the algorithms for calculating the differential geometric properties {t,n,b1,b2,b3,k1,k2,k3,k4} along-with geodesic curvature and geodesic torsion of the transversal intersection curve of four hypersurfaces (given…
Sequence transformations accomplish an acceleration of convergence or a summation in the case of divergence by detecting and utilizing regularities of the elements of the sequence to be transformed. For sufficiently large indices, certain…
Reflector-normal angles and reflector-curvature parameters are the principal geometric attributes used in seismic interpretation for characterizing the orientations and shapes, respectively, of geological reflecting surfaces. Commonly, the…
Let Gamma be a congruence subgroup of the Picard modular group of an imaginary number field k, and let D be the associated symmetric space. We describe a method to compute the integral cohomology of the locally symmetric space Gamma\D. The…
Clifford geometric algebras of multivectors are introduced which exhibit a bilinear form which is not necessarily symmetric. Looking at a subset of bi-vectors in CL(K^{2n},B), we proof that theses elements generate the Hecke algebra…
Symmetries impose structure on the Hilbert space of a quantum mechanical model. The mathematical units of this structure are the irreducible representations of symmetry groups and I consider how they function as conceptual units of…
Space-times which allow a slicing into homogeneous spatial hypersurfaces generalize the usual Bianchi models. One knows already that in these models the Bianchi type may change with time. Here we show which of the changes really appear. To…
The isotropic harmonic oscillator and the Kepler-Coulomb system are pivotal models in the Sciences. They are two examples of second-order (maximally) superintegrable (Hamiltonian) systems. These systems are classified in dimension two. A…
A class of decoherence schemes is described for implementing the principles of generalized quantum theory in reparametrization-invariant `hyperbolic' models such as minisuperspace quantum cosmology. The connection with sum-over-histories…
In this paper, we study the smooth isometric immersion of a complete, simply connected surface with a negative Gauss curvature into the three-dimensional Euclidean space. A fundamental and longstanding problem is to find a sufficient…
We employ Chen's conformal invariant quantity [8, Theorem 1] in combination with the Chern-Gauss-Bonnet formulas to obtain expressions for the renormalized area of asymptotically minimal hypersurfaces in the $(2n+1)$-dimensional hyperbolic…
In this thesis we consider a way to construct a rich family of compact Riemann Surfaces in a combinatorial way. Given a 3-regualr graph with orientation, we construct a finite-area hyperbolic Riemann surface by gluing triangles according to…
A connected regular surface in Lorentz-Minkowski 3-space is called a mixed type surface if the spacelike, timelike and lightlike point sets are all non-empty. Lightlike points on mixed type surfaces may be regarded as singular points of the…
An affine hypersurface is said to admit a pointwise symmetry, if there exists a subgroup of the automorphism group of the tangent space, which preserves (pointwise) the affine metric h, the difference tensor K and the affine shape operator…
These notes provide an introduction to Giroux's theory of convex surfaces in contact 3-manifolds and its simplest applications. They put a special emphasis on pictures and discussions of explicit examples. The first goal is to explain why…
Multicriticality of the gonihedric model in 2+1 dimensions is investigated numerically. The gonihedric model is a fully frustrated Ising magnet with the finely tuned plaquette-type (four-body and plaquette-diagonal) interactions, which…
We define a notion of isotropic surfaces in $\mathbb{O}$, i.e. on which some canonical symplectic forms vanish. Using the cross-product in $\mathbb{O}$ we define a map $\rho\colon Gr\_2(\mathbb{O})\to S^6$ from the Grassmannian of…