Search results for "Constant curvature"
showing 9 items of 9 documents
Anharmonicity deformation and curvature in supersymmetric potentials
1994
An algebraic description of the class of 1D supersymmetric shape invariant potentials is investigated in terms of the shape-invariant-potential (SIP) deformed algebra, the generators of which act both on the dynamical variable and on the parameters of the potentials. The phase space geometry associated with SIP's is studied by means of a coherent state (SIP-CS) path integral and the ray metric of the SIP-CS manifold. The anharmonicity of SIP's results in a inhomogeneous phase space manifold with one Killing vector and with a modified symplectic Kahler structure, and it induces a non constant curvature into the generalized phase space. Analogous results from the phase space geometry of someq…
Relation between quasirigidity andL-rigidity in space-times of constant curvature and weak fields
1997
The relation between quasirigidity andL-rigidity in space-times of constant nonzero curvature and in space-times with small curvature (weak fields) is studied. The covariant expansion of bitensors about a point is considered. We obtain an increase in the order of magnitude, underL-rigidity conditions, of the rate of change with respect to a comoving orthonormal frame of the linear momentum, angular momentum, and reduced multipole moments of the energy-momentum tensor. Thus,L-rigidity leads to quasirigidity in such space-times.
Salkowski curves revisited: A family of curves with constant curvature and non-constant torsion
2009
In the paper [Salkowski, E., 1909. Zur Transformation von Raumkurven, Mathematische Annalen 66 (4), 517-557] published one century ago, a family of curves with constant curvature but non-constant torsion was defined. We characterize them as space curves with constant curvature and whose normal vector makes a constant angle with a fixed line. The relation between these curves and rational curves with double Pythagorean hodograph is studied. A method to construct closed curves, including knotted curves, of constant curvature and continuous torsion using pieces of Salkowski curves is outlined.
Riemann’s Result and Consequences for Physics and Philosophy
2020
Riemann commented on his main result as follows: “The common character of those manifolds whose curvature is constant may also be expressed thus: that figures may be viewed in them without stretching. For clearly figures could not be arbitrarily shifted and turned around in them if the curvature at each point were not the same in all directions at one point as at another, and consequently the same constructions can be made from it; whence it follows that in aggregates with constant curvature, figures may have any arbitrary position given them. The measure-relations of these manifolds depend only on the value of the curvature, and in relation to the analytic expression it may be remarked tha…
Hamiltonian structural analysis of curved beams with or without generalized two-parameter foundation
2013
The solution of curved Timoshenko beams with or without generalized two-parameter elastic foundation is presented. Beam can be subjected to any kind of loads and imposed external actions, distributed or concentrated along the beam. It can have external and internal restraints and any kind of internal kinematical or mechanical discontinuity. Moreover, the beam may have any spatial curved geometry, by dividing the entire structure into segments of constant curvature and constant elastic properties, each segment resting or not on elastic foundation. The foundation has six parameters like a generalized Winkler soil with the addition of other two parameters involving the link between settlements…
Radial conformal motions in Minkowski space–time
1999
A study of radial conformal Killing fields (RCKF) in Minkowski space-time is carried out, which leads to their classification into three disjointed classes. Their integral curves are straight or hyperbolic lines admitting orthogonal surfaces of constant curvature, whose sign is related to the causal character of the field. Otherwise, the kinematic properties of the timelike RCKF are given and their applications in kinematic cosmology is discussed.
A kinematic method to obtain conformal factors
2000
Radial conformal motions are considered in conformally flat space-times and their properties are used to obtain conformal factors. The geodesic case leads directly to the conformal factor of Robertson-Walker universes. General cases admitting homogeneous expansion or orthogonal hypersurfaces of constant curvature are analyzed separately. When the two conditions above are considered together a subfamily of the Stephani perfect fluid solutions, with acceleration Fermi-Walker propagated along the flow of the fluid, follows. The corresponding conformal factors are calculated and contrasted with those associated with Robertson-Walker space-times.
Graded metrics adapted to splittings
1997
Homogeneous graded metrics over split ℤ2-graded manifolds whose Levi-Civita connection is adapted to a given splitting, in the sense recently introduced by Koszul, are completely described. A subclass of such is singled out by the vanishing of certain components of the graded curvature tensor, a condition that plays a role similar to the closedness of a graded symplectic form in graded symplectic geometry: It amounts to determining a graded metric by the data {g, ω, Δ′}, whereg is a metric tensor onM, ω 0 is a fibered nondegenerate skewsymmetric bilinear form on the Batchelor bundleE → M, and Δ′ is a connection onE satisfying Δ′ω = 0. Odd metrics are also studied under the same criterion an…
Adaptive Control of Soft Robots Based on an Enhanced 3D Augmented Rigid Robot Matching
2021
Despite having proven successful in generating precise motions under dynamic conditions in highly deformable soft-bodied robots, model based techniques are also prone to robustness issues connected to the intrinsic uncertain nature of the dynamics of these systems. This letter aims at tackling this challenge, by extending the augmented rigid robot formulation to a stable representation of three dimensional motions of soft robots, under Piecewise Constant Curvature hypothesis. In turn, the equivalence between soft-bodied and rigid robots permits to derive effective adaptive controllers for soft-bodied robots, achieving perfect posture regulation under considerable errors in the knowledge of …