We discuss the interpretation of path integral optimization as a uniformization problem in even dimensions. This perspective allows for systematical construction higher-dimensional complexity holographic conformal field theories terms Q-curvature actions. explore properties and consequences these actions from programme, tensor networks penalty factors. Moreover, context recently proposed optimi...

The object of this paper is to study $(epsilon)$-Lorentzian para-Sasakian manifolds. Some typical identities for the curvature tensor and the Ricci tensor of $(epsilon)$-Lorentzian para-Sasakian manifold are investigated. Further, we study globally $phi$-Ricci symmetric and weakly $phi$-Ricci symmetric $(epsilon)$-Lorentzian para-Sasakian manifolds and obtain interesting results.

Examples of conformal dynamo maps have been presented earlier [Phys Plasmas 14(2007)] where fast dynamos in twisted magnetic flux tubes in Riemannian manifolds were obtained. This paper shows that conformal maps, under the Floquet condition, leads to coincidence between exponential stretching or Lyapunov exponent, conformal factor of fast dynamos. Unfolding conformal dynamo maps can be obtained...

We define a conformally invariant action S on gauge connections closed pseudo-Riemannian manifold M of dimension 6. At leading order this is quadratic in the connection. The Euler-Lagrange equations S, with respect to variation connection, provide higher-order analogue (source-free) Yang-Mills equations. For any connection A M, we S(A) by first defining Lagrangian density associated A. This not...

A “conformal tensor” is constructed from the metric tensor gMN (or Vielbein e A M ) and is invariant against Weyl rescaling gMN → egMN (or eM → eeM ). Moreover, it vanishes if and only if the space is conformally flat, gMN = e ηMN (or e A M = eδ M ). In dimension four or greater the conformal tensor is the Weyl tensor. In three dimensions the Weyl tensor vanishes identically, while the Cotton t...

The integrability conditions for the existence of a conformal Killing-Yano tensor of arbitrary order are worked out in all dimensions and expressed in terms of the Weyl tensor. As a consequence, the integrability conditions for the existence of a Killing-Yano tensor are also obtained. By means of such conditions, it is shown that in certain Einstein spaces one can use a conformal Killing-Yano t...

We consider a certain variant of teleparallel gravity: a differential manifold endowed with a smooth coframe field. The differentialgeometric structure on the manifold can be characterized by the objects of anholonomity and its derivative objects of curvature. We construct a full list of the first and second order SO(1, 3)-covariants (oneand two-indexed quantities) and a most general quasi-line...

We construct explicit left invariant quaternionic contact structures on Lie groups with zero and non-zero torsion, and with non-vanishing quaternionic contact conformal curvature tensor, thus showing the existence of quaternionic contact manifolds not locally quaternionic contact conformal to the quaternionic sphere. We present a left invariant quaternionic contact structure on a seven dimensio...

Abstract Motivated by constant-G theory, we introduce a one-parameter family of scalar–tensor theories as an extension theory in which the conformal symmetry is cosmological attractor. Since model has coupling function negative curvature, expect spontaneous scalarization to occur and that parameter can be constrained pulsar timing measurements. Modeling neutron stars with realistic equations st...