Search engine for discovering works of Art, research articles, and books related to Art and Culture
Javascript must be enabled to continue!
On curvature tensors of Norden and metallic pseudo-Riemannian manifolds
View through CrossRef
AbstractWe study some properties of curvature tensors of Norden and, more generally, metallic pseudo-Riemannian manifolds. We introduce the notion of J-sectional and J-bisectional curvature of a metallic pseudo-Riemannian manifold (M, J, g) and study their properties.We prove that under certain assumptions, if the manifold is locally metallic, then the Riemann curvature tensor vanishes. Using a Norden structure (J, g) on M, we consider a family of metallic pseudo-Riemannian structures {Ja,b}a,b∈ℝ and show that for a ≠ 0, the J-sectional and J-bisectional curvatures of M coincide with the Ja,b-sectional and Ja,b-bisectional curvatures, respectively. We also give examples of Norden and metallic structures on ℝ2n.
Title: On curvature tensors of Norden and metallic pseudo-Riemannian manifolds
Description:
AbstractWe study some properties of curvature tensors of Norden and, more generally, metallic pseudo-Riemannian manifolds.
We introduce the notion of J-sectional and J-bisectional curvature of a metallic pseudo-Riemannian manifold (M, J, g) and study their properties.
We prove that under certain assumptions, if the manifold is locally metallic, then the Riemann curvature tensor vanishes.
Using a Norden structure (J, g) on M, we consider a family of metallic pseudo-Riemannian structures {Ja,b}a,b∈ℝ and show that for a ≠ 0, the J-sectional and J-bisectional curvatures of M coincide with the Ja,b-sectional and Ja,b-bisectional curvatures, respectively.
We also give examples of Norden and metallic structures on ℝ2n.
Related Results
Biquadratic Tensors: Eigenvalues and Structured Tensors
Biquadratic Tensors: Eigenvalues and Structured Tensors
The covariance tensors in statistics and Riemann curvature tensor in relativity theory are both biquadratic tensors that are weakly symmetric, but not symmetric in general. Motivat...
Riemannian Curvature of a Sliced Contact Metric Manifold
Riemannian Curvature of a Sliced Contact Metric Manifold
Contact geometry become a more important issue in the mathematical world with the works which had done in the 19th century. Many mathematicians have made studies on contact manifol...
STUDY OF DIFFERENT TYPES OF CONNECTION IN VARIOUS DIFFERENTIABLE MANIFOLD
STUDY OF DIFFERENT TYPES OF CONNECTION IN VARIOUS DIFFERENTIABLE MANIFOLD
The present work investigates numerous types of affine connections defined on differentiable manifolds, with a focus on Lorentzian para-Sasakian (LP-Sasakian) manifolds with non-Le...
LVM manifolds and lck metrics
LVM manifolds and lck metrics
Abstract
In this paper, we compare two type of complex non-Kähler manifolds : LVM and lck manifolds. First, lck manifolds (for locally conformally Kähler manifolds) admit a...
Connection, Curvature, and Holonomy for Ehresmann Connections on Riemannian Submersions
Connection, Curvature, and Holonomy for Ehresmann Connections on Riemannian Submersions
We study Ehresmann connections on smooth fibered manifolds equipped with Riemannian submersion structures\[\pi : M \rightarrow Z,\]focusing on the interaction between horizontal tr...
Pointwise semi-slant Riemannian maps into almost Hermitian manifolds and Casorati inequalities
Pointwise semi-slant Riemannian maps into almost Hermitian manifolds and Casorati inequalities
UDC 514
As a natural generalization of slant submanifolds [B.-Y. Chen, Bull. Austral. Math. Soc., 41, No. 1, 135 (1990)], slant submersions [B. Şahin, Bull. Math. Soc. Sci. Math....
Curvature tensors of higher-spin gauge theories derived from general Lagrangian densities
Curvature tensors of higher-spin gauge theories derived from general Lagrangian densities
Curvature tensors of higher-spin gauge theories have been known for some time. In the past, they were postulated using a generalization of the symmetry properties of the Riemann te...
Even-Order Pascal Tensors Are Positive-Definite
Even-Order Pascal Tensors Are Positive-Definite
In this paper, we show that even-order Pascal tensors are positive-definite, and odd-order Pascal tensors are strongly completely positive. The significance of these is that our in...