15 research outputs found
Stanilov-Tsankov-Videv Theory
We survey some recent results concerning Stanilov-Tsankov-Videv theory,
conformal Osserman geometry, and Walker geometry which relate algebraic
properties of the curvature operator to the underlying geometry of the
manifold.Comment: This is a contribution to the Proceedings of the 2007 Midwest
Geometry Conference in honor of Thomas P. Branson, published in SIGMA
(Symmetry, Integrability and Geometry: Methods and Applications) at
http://www.emis.de/journals/SIGMA
Complete curvature homogeneous pseudo-Riemannian manifolds
We exhibit 3 families of complete curvature homogeneous pseudo-Riemannian
manifolds which are modeled on irreducible symmetric spaces and which are not
locally homogeneous. All of the manifolds have nilpotent Jacobi operators; some
of the manifolds are, in addition, Jordan Osserman and Jordan Ivanov-Petrova.Comment: Update paper to fix misprints in original versio
Examples of signature (2,2) manifolds with commuting curvature operators
We exhibit Walker manifolds of signature (2,2) with various commutativity
properties for the Ricci operator, the skew-symmetric curvature operator, and
the Jacobi operator. If the Walker metric is a Riemannian extension of an
underlying affine structure A, these properties are related to the Ricci tensor
of A
Stanilov-Tsankov-Videv Theory
We survey some recent results concerning Stanilov-Tsankov-Videv theory, conformal Osserman geometry, and Walker geometry which relate algebraic properties of the curvature operator to the underlying geometry of the manifold
Curvature homogeneous spacelike Jordan Osserman pseudo-Riemannian manifolds
Let s be at least 2. We construct Ricci flat pseudo-Riemannian manifolds of
signature (2s,s) which are not locally homogeneous but whose curvature tensors
never the less exhibit a number of important symmetry properties. They are
curvature homogeneous; their curvature tensor is modeled on that of a local
symmetric space. They are spacelike Jordan Osserman with a Jacobi operator
which is nilpotent of order 3; they are not timelike Jordan Osserman. They are
k-spacelike higher order Jordan Osserman for ; they are k-timelike
higher order Jordan Osserman for , and they are not k timelike
higher order Jordan Osserman for .Comment: Update bibliography, fix minor misprint
5G-CLARITY : 5G-advanced private networks integrating 5GNR, WiFi, and LiFi
The future of the manufacturing industry highly depends on digital systems that transform existing production and monitoring systems into autonomous systems fulfilling stringent requirements in terms of availability, reliability, security, low latency, and positioning with high accuracy. In order to meet such requirements, private 5G networks are considered as a key enabling technology. In this article, we introduce the 5G-CLARITY system that integrates 5GNR, WiFi, and LiFi access networks, and develops novel management enablers to operate 5G-Advanced private networks. We describe three core features of 5G-CLARITY, including a multi-connectivity framework, a high-precision positioning server, and a management system to orchestrate private network slices. These features are evaluated by means of packet-level simulations and an experimental testbed demonstrating the ability of 5G-CLARITY to police access network traffic, to achieve centimeter-level positioning accuracy, and to provision private network slices in less than one minute