Results 261 to 270 of about 464,650 (293)

Hilbert polynomials and Arveson's curvature invariant [PDF]

Journal of Functional Analysis, 2003
The author proves some formulas relating the leading coefficients of Hilbert polynomials for invariant subspaces of the symmetric Fock space and the curvature invariant for the corresponding coinvariant subspaces. A generalization of the Gauss-Bonnet-Chern formula from the homogeneous polynomially generated submodules to arbitrary polynomially ...
Fang, Xiang, Xiang Fang
exaly   +3 more sources

Complete Nevanlinna–Pick kernels and the curvature invariant

Annali Di Matematica Pura Ed Applicata
We consider a unitarily invariant complete Nevanlinna-Pick kernel denoted by $s$ and a commuting $d$-tuple of bounded operators $T = (T_{1}, \dots, T_{d})$ satisfying a natural contractivity condition with respect to $s$. We associate with $T$ its curvature invariant which is a non-negative real number bounded above by the dimension of a defect space ...
Abhay Jindal
exaly   +5 more sources

On the Flag Curvature of Invariant Randers Metrics [PDF]

Mathematical Physics Analysis and Geometry, 2008
In the present paper, the flag curvature of invariant Randers metrics on homogeneous spaces and Lie groups is studied. We first give an explicit formula for the flag curvature of invariant Randers metrics arising from invariant Riemannian metrics on homogeneous spaces and, in special case, Lie groups.
Hamid Reza Salimi Moghaddam
exaly   +3 more sources

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Topological invariants and curvature

2022
Summary: It is widely known that the fundamental group of a Lie group, and in general a symmetric space, is abelian. In the current paper it is demonstrated that any finitely generated abelian group is the fundamental group of a compact Lie group. In addition, it is proved that for any arbitrary group there is a differentiable manifold of dimension ...
Toomanian, Megerdich, Arab, Gholam Hossein   +1 more
openaire   +2 more sources

Gaussian-curvature-derived invariants for isometry

Science China Information Sciences, 2012
Surface deformations without tearing or stretching, preserving the intrinsic properties, are called isometries. This paper presents a new definition of Gaussian curvature moments (GCMs) by the integral of n power of Gaussian curvature. Then a series of moment invariants, called Gaussian curvature moment invariants (GCMIs), are derived via GCMs.
Weiguo Cao, Ping Hu, Yujie Liu, Ming Gong 0001, Hua Li 0009   +4 more
openaire   +2 more sources

Tensor Invariants for Gravitational Curvatures

2021
<p>The tensor invariants (or invariants of tensors) for gravity gradient tensors (GGT, the second-order derivatives of the gravitational potential (GP)) have the advantage of not changing with the rotation of the corresponding coordinate system, which were widely applied in the study of gravity field (e.g., recovery of global gravity ...
Xiao-Le Deng, Wen-Bin Shen, Meng Yang, Jiangjun Ran   +3 more
openaire   +1 more source

Invariant curvature-based Fourier shape descriptors

Journal of Visual Communication and Image Representation, 2012
Shape descriptors have demonstrated encouraging potential for retrieving images based on image content, and a number of them have been reported in the literature. Nevertheless, most of the reported descriptors are still face accuracy and computational challenges.
Otman Basir
exaly   +2 more sources

Invariance Conditions for Random Curvature Models

Methodology And Computing In Applied Probability, 2003
The author introduces a class of probability laws suggesed by the geometric optics of the human eye. These models are concerned with the representation of random corneal curvature measurements \(y\) indexed by concentric equally-spaced locations \(v= \{\theta_1,\theta_2,\dots, \theta_\ell\}\).
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On the Pick Invariant, the Affine mean Curvature and the Gauss Curvature of Affine Surfaces

Results in Mathematics, 1991
By departing from the so-called Affine Theorema Egregium for a nondegenerate unimodular affine surface \(M^ 2\subset\mathbb{R}^ 3\), which states that \({\mathfrak k}=H+J\), where \({\mathfrak k}\) is the Gauss curvature of the affine metric, \(H\) the affine mean curvature and \(J\) the Pick invariant, the authors study those affine surfaces where \({\
Dillen, Franki, Martinez, Antonio, Milan, Francisco, Garcia Santos, Florentino, Vrancken, Luc   +4 more
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Segmentation of surface curvature using a photometric invariant

Proceedings of IEEE Conference on Computer Vision and Pattern Recognition CVPR-94, 1994
Gaussian curvature is an intrinsic local shape characteristic of a smooth object surface that is invariant to orientation of the object in 3-D space and viewpoint. Accurate determination of the sign of Gaussian curvature at each point on a smooth object surface (i.e., the identification of hyperbolic, elliptical and parabolic points) can provide very ...
Lawrence B. Wolff, Joel Fan
openaire   +2 more sources