The holographic Weyl anomaly associated to Chern-Simons gravity in 2n + 1 dimensions is proportional to the Euler term in 2n dimensions, with no contributions from the Weyl tensor. We compute the holographic energy-momentum tensor associated to ChernSimons gravity directly from the action, in an arbitrary odd-dimensional spacetime. We show, in particular, that the counterterms rendering the act...

‎In this study‎, ‎properties of spectral characteristic are investigated for‎ ‎singular Sturm-Liouville operators in the case where an eigen‎ ‎parameter not only appears in the differential equation but is‎ ‎also linearly contained in the jump conditions‎. ‎Also Weyl function‎ ‎for considering operator has been defined and the theorems which‎ ‎related to uniqueness of solution of inverse proble...

Pseudo-Riemannian geometry is, to a large extent, the study of the Levi-Civita connection, which is the unique torsion-free connection compatible with the metric structure. There are, however, other affine connections which arise in different contexts, such as conformal geometry, contact structures, Weyl structures, and almost Hermitian geometry. In this book, we reverse this point of view and ...

We extend the non-perturbative time-dependent bosonic string action of [3] to a N = 1 supersymmetric world sheet action with graviton background, and assume a superpotential, function of the time super coordinate. The use of (super)strings for the description of cosmological events suggests that String Theory might become observable, given the huge amount of cosmological data [1]. String Cosmol...

A review of the construction of a Weyl-invariant spinning-membrane action that is polynomial in the fields, without a cosmological constant term, comprised of quadratic and quartic-derivative terms, and where supersymmetry is linearly realized, is presented. The action is invariant under a modified supersymmetry transformation law which is derived from a new Q+K + S sum-rule based on the 3D-sup...

In the multiscalar-metric frameworks, issues of vacuum energy/cosmological constant (CC) screening due to Weyl-scale enhancement Diff gauge symmetry, along with emergence massive dark gravity components through gravitational Higgs mechanism are considered. A generic model is developed, two extreme versions particular interest based on General Relativity (GR) and its classically equivalent Weyl ...

In this paper, we study certain compact 4-manifolds with non-negative sectional curvature K. If s is the scalar curvature and W+ is the self-dual part of Weyl tensor, then it will be shown that there is no metric g on S2 × S2 with both (i) K > 0 and (ii) 1 6 s−W+ ≥ 0. We also investigate other aspects of 4-manifolds with non-negative sectional curvature. One of our results implies a theorem of ...

In this paper we study the embedding of Riemannian manifolds in low codimension. The well-known result of Nash and Kuiper [21, 20] says that any short embedding in codimension one can be uniformly approximated by C isometric embeddings. This statement clearly cannot be true for C embeddings in general, due to the classical rigidity in the Weyl problem. In fact Borisov extended the latter to emb...

We present unique solutions of the Seiberg-Witten Monopole Equations in which the U(1) curvature is covariantly constant, the monopole Weyl spinor consists of a single constant component, and the 4-manifold is a product of two Riemann surfaces of genuses p1 and p2. There are p1 − 1 magnetic vortices on one surface and p2−1 electric ones on the other, with p1 + p2 ≥ 2 (p1 = p2 = 1 being excluded...