The Experts below are selected from a list of 23970 Experts worldwide ranked by ideXlab platform
David Kastor - One of the best experts on this subject based on the ideXlab platform.
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the riemann lovelock Curvature Tensor
Classical and Quantum Gravity, 2012Co-Authors: David KastorAbstract:In order to study the properties of Lovelock gravity theories in low dimensions, we define the kth-order Riemann–Lovelock Tensor as a certain quantity having a total 4k-indices, which is kth order in the Riemann Curvature Tensor and shares its basic algebraic and differential properties. We show that the kth-order Riemann–Lovelock Tensor is determined by its traces in dimensions 2k ⩽ D < 4k. In D = 2k + 1 this identity implies that all solutions of pure kth-order Lovelock gravity are ‘Riemann–Lovelock’ flat. It is verified that the static, spherically symmetric solutions of these theories, which are missing solid angle spacetimes, indeed satisfy this flatness property. This generalizes results from Einstein gravity in D = 3, which corresponds to the k = 1 case. We speculate about some possible further consequences of Riemann–Lovelock Curvature.
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the riemann lovelock Curvature Tensor
arXiv: High Energy Physics - Theory, 2012Co-Authors: David KastorAbstract:In order to study the properties of Lovelock gravity theories in low dimensions, we define the kth-order Riemann-Lovelock Tensor as a certain quantity having a total 4k-indices, which is kth-order in the Riemann Curvature Tensor and shares its basic algebraic and differential properties. We show that the kth-order Riemann-Lovelock Tensor is determined by its traces in dimensions 2k \le D <4k. In D=2k+1 this identity implies that all solutions of pure kth-order Lovelock gravity are `Riemann-Lovelock' flat. It is verified that the static, spherically symmetric solutions of these theories, which are missing solid angle space times, indeed satisfy this flatness property. This generalizes results from Einstein gravity in D=3, which corresponds to the k=1 case. We speculate about some possible further consequences of Riemann-Lovelock Curvature.
A Hoglund - One of the best experts on this subject based on the ideXlab platform.
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the lanczos potential for the weyl Curvature Tensor existence wave equation and algorithms
Proceedings of The Royal Society A: Mathematical Physical and Engineering Sciences, 1997Co-Authors: S B Edgar, A HoglundAbstract:In the last few years renewed interest in the 3–Tensor potential L abc proposed by Lanczos for the Weyl Curvature Tensor has not only clarified and corrected Lanczos9s original work, but generalized the concept in a number of ways. In this paper we first of all carefully summarize and extend some aspects of these results, make some minor corrections, and clarify some misunderstandings in the literature. The following new results are also presented. The (computer checked) complicated second–order partial differential equation for the 3–potential, in arbitrary gauge, for Weyl candidates satisfying Bianchi–type equations is given, in those n–dimensional spaces (with arbitrary signature) for which the potential exists; this is easily specialized to Lanczos potentials for the Weyl Curvature Tensor. It is found that it is only in four–dimensional spaces (with arbitrary signature) that the nonlinear terms disappear and that certain awkward second–order derivative terms cancel; for four–dimensional spacetimes (with Lorentz signature), this remarkably simple form was originally found by Illge, using spinor methods. It is also shown that, for most four–dimensional vacuum spacetimes, any 3–potential in the Lanczos gauges which satisfies a simple homogeneous wave equation must be a Lanczos potential for the non–zero Weyl Curvature Tensor of the background vacuum spacetime. This result is used to prove that the form of a possible Lanczos potential recently proposed by Dolan and Kim for a class of vacuum spacetimes is in fact a genuine Lanczos potential for these spacetimes.
Hans-peter Seidel - One of the best experts on this subject based on the ideXlab platform.
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Exact and interpolatory quadratures for Curvature Tensor estimation
Computer Aided Geometric Design, 2007Co-Authors: Torsten Langer, Alexander Belyaev, Hans-peter SeidelAbstract:The computation of the Curvature of smooth surfaces has a long history in differential geometry and is essential for many geometric modeling applications such as feature detection. We present a novel approach to calculate the mean Curvature from arbitrary normal Curvatures. Then, we demonstrate how the same method can be used to obtain new formulae to compute the Gaussian Curvature and the Curvature Tensor. The idea is to compute the Curvature integrals by a weighted sum by making use of the periodic structure of the normal Curvatures to make the quadratures exact. Finally, we derive an approximation formula for the Curvature of discrete data like meshes and show its convergence if quadratically converging normals are available.
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exact and approximate quadratures for Curvature Tensor estimation
Vision Modeling and Visualization, 2005Co-Authors: Torsten Langer, Alexander Belyaev, Hans-peter SeidelAbstract:Accurate estimations of geometric properties of a surface from its discrete approximation are important for many computer graphics and geometric modeling applications. In this paper, we derive exact quadrature formulae for mean Curvature, Gaussian Curvature, and the Taubin integral representation of the Curvature Tensor. The exact quadratures are then used to obtain reliable estimates of the Curvature Tensor of a smooth surface approximated by a dense triangle mesh. The proposed method is fast and easy to implement. It is highly competitive with conventional Curvature Tensor estimation approaches. Additionally, we show that the Curvature Tensor approximated as proposed by us converges towards the true Curvature Tensor as the edge lengths tend to zero.
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normal based estimation of the Curvature Tensor for triangular meshes
Pacific Conference on Computer Graphics and Applications, 2004Co-Authors: Holger Theisel, C Rossi, Rhaleb Zayer, Hans-peter SeidelAbstract:We introduce a new technique for estimating the Curvature Tensor of a triangular mesh. The input of the algorithm is only a single triangle equipped with its (exact or estimated) vertex normals. This way we get a smooth junction of the Curvature Tensor inside each triangle of the mesh. We show that the error of the new method is comparable with the error of a cubic fitting approach if the incorporated normals are estimated. If the exact normals of the underlying surface are available at the vertices, the error drops significantly. We demonstrate the applicability of the new estimation at a rather complex data set.
A Taleshian - One of the best experts on this subject based on the ideXlab platform.
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on conformal and quasi conformal Curvature Tensors of an n κ quasi einstein manifold
Communications of The Korean Mathematical Society, 2012Co-Authors: Aliakbar Hosseinzadeh, A TaleshianAbstract:We consider -quasi Einstein manifolds satisfying the conditions , , , and where , , and denote the conformal Curvature Tensor, the quasi-conformal Curvature Tensor, the projective Curvature Tensor and the pseudo projective Curvature Tensor, respectively.
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conharmonic Curvature Tensor on contact metric manifolds
International Scholarly Research Notices, 2011Co-Authors: Sujit Ghosh, A TaleshianAbstract:The object of the present paper is to characterize ()-contact metric manifolds satisfying certain Curvature conditions on the conharmonic Curvature Tensor. In this paper we study conharmonically symmetric, -conharmonically flat, and -conharmonically flat ()-contact metric manifolds.
Jose M M Senovilla - One of the best experts on this subject based on the ideXlab platform.
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a local potential for the weyl Tensor in all dimensions
Classical and Quantum Gravity, 2004Co-Authors: Brian S Edgar, Jose M M SenovillaAbstract:In all dimensions n ≥ 4 and arbitrary signature, we demonstrate the existence of a new local potential - a double (2, 3)-form, Pabcde - for the Weyl Curvature Tensor Cabcd, and more generally for a ...
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a local potential for the weyl Tensor in all dimensions
arXiv: General Relativity and Quantum Cosmology, 2004Co-Authors: Brian S Edgar, Jose M M SenovillaAbstract:In all dimensions and arbitrary signature, we demonstrate the existence of a new local potential -- a double (2,3)-form -- for the Weyl Curvature Tensor, and more generally for all Tensors with the symmetry properties of the Weyl Curvature Tensor. The classical four-dimensional Lanczos potential for a Weyl Tensor -- a double (2,1)-form -- is proven to be a particular case of the new potential: its double dual.
