نتایج جستجو برای: curvature tensor
تعداد نتایج: 83044 فیلتر نتایج به سال:
We analytically derive the covariant form of Riemann (curvature) tensor for homogeneous metric-affine cosmologies. That is, we present, in a cosmological setting, most general full including also its non-Riemannian pieces which are associated to spacetime torsion and non-metricity. Having done so compute list curvature by-products such as Ricci tensor, homothetic curvature, scalar, Einstein etc...
In this paper, we study Kropina metrics with isotropic scalar curvature. First, obtain the expressions of Ricci curvature tensor and Then, characterize on by analysis.
Together with spaces of constant sectional curvature and products of a real line with a manifold of constant curvature, the socalled Egorov spaces and ε-spaces exhaust the class of n-dimensional Lorentzian manifolds admitting a group of isometries of dimension at least 1 2n(n − 1) + 1, for almost all values of n [Patrangenaru V., Geom. Dedicata 102 (2003), 25–33]. We shall prove that the curvat...
We investigate geodesics in specific Kundt type N (or conformally flat) solutions to Einstein’s equations. Components of the curvature tensor in parallelly transported tetrads are then explicitly evaluated and analyzed. This elucidates some interesting global properties of the spacetimes, such as an inherent rotation of the wave-propagation direction, or the character of singularities. In parti...
There is a 14-dimensional algebraic curvature tensor which is Jacobi–Tsankov (i.e. J (x)J (y) = J (y)J (x) for all x, y) but which is not 2-step Jacobi nilpotent (i.e. J (x)J (y) = 0 for some x, y); the minimal dimension where this is possible is 14. We determine the group of symmetries of this tensor and show that it is geometrically realizable by a wide variety of pseudo-Riemannian manifolds ...
We examine theories of gravity which include finitely many coupled scalar fields with arbitrary couplings to the curvature (wavemaps). We show that the most general scalar-tensor σ-model action is conformally equivalent to general relativity with a minimally coupled wavemap with a particular target metric. Inflation on the source manifold is then shown to occur in a novel way due to the combine...
We describe a method to generate blend surfaces which t with continuous curvature to the primary surfaces. This blend surface is obtained as the bicubic tensor spline minimizing a variational problem. Among all the bicubic tensor splines which give a curvature continuous blend surface, the one is chosen which minimizes a bilinear functional. In Section 2 we summarize and extend the results of a...
There is a 14-dimensional algebraic curvature tensor which is Jacobi–Tsankov (i.e. J (x)J (y) = J (y)J (x) for all x, y) but which is not 2-step Jacobi nilpotent (i.e. J (x)J (y) 6= 0 for some x, y); the minimal dimension where this is possible is 14. We determine the group of symmetries of this tensor and show that it is geometrically realizable by a wide variety of pseudo-Riemannian manifolds...
This paper presents an algebraically extended 2D image representation. Combining methods of tensor algebra, monogenic signal and quadrature filter, this novel image representation can be derived as the monogenic extension of a curvature tensor. From it, the monogenic signal and the monogenic curvature signal for modeling intrinsically one and two dimensional (i1D/i2D) structures are obtained as...
Let R be an algebraic curvature tensor for a non-degenerate inner product of signature (p, q) where q ≥ 5. If π is a spacelike 2 plane, let R(π) be the associated skewsymmetric curvature operator. We classify the algebraic curvature tensors so R(·) has constant rank 2 and show these are geometrically realizable by hypersurfaces in flat spaces. We also classify the Ivanov-Petrova algebraic curva...
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