This paper relates the boundary term in the Chern-Gauss-Bonnet formula on 4-manifolds M with the renormalized volume V , as defined in the AdS/CFT correspondence, for asymptotically hyperbolic Einstein metrics on M . In addition we show that the differential or variation dV of V , or equivalently the variation of the L norm of the Weyl curvature, is intrinsically determined by the conformal inf...

Any Riemannian manifold has a canonical collection of valuations (finitely additive measures) attached to it, known as the intrinsic volumes or Lipschitz–Killing valuations. They date back remarkable discovery H. Weyl that coefficients tube volume polynomial are invariants metric. As consequence, behave naturally under isometric immersions. This phenomenon, subsequently observed in number diffe...

A six dimensional manifold of symmetric signature (3,3) is proposed as a space structure for building combined theory gravity and electromagnetism. Special metric tensor proposed, yielding the which combines properties Riemann, Weyl Finsler spaces. Geodesic line equations are constructed where coefficients can be divided into depending on (relating to gravitational interaction) vector field ele...

In the first part of this paper, some theorems are given for a Riemannian manifold with semi-symmetric metric connection. In the second part of it, some special vector fields, for example, torse-forming vector fields, recurrent vector fields and concurrent vector fields are examined in this manifold. We obtain some properties of this manifold having the vectors mentioned above.

We consider the Laplace--Beltrami operator on a three-dimensional Riemannian manifold perturbed by potential from Kato class and study whether various forms of Weyl's law remain valid under this perturbation. show that pointwise Weyl holds, modified an additional term, for any with standard sharp remainder term. The term is always lower order than leading but it may or not be In particular, we ...

LetW be a finite irreducible real reflection group, which is a Coxeter group. A primitive derivation D, introduced and studied by K. Saito (e.g., [4]), plays a crucial role in the theory of differential forms with logarithmic poles along the Coxeter arrangement. For example, we may describe the contact order filtration of the logarithmic derivation module using the primitive derivations ([10, 1...

In this paper we will determine the multiple point manifolds of certain self-transverse immersions in Euclidean spaces. Following the triple points, these immersions have a double point self-intersection set which is the image of an immersion of a smooth 5-dimensional manifold, cobordant to Dold manifold $V^5$ or a boundary. We will show there is an immersion of $S^7times P^2$ in $mathbb{R}^{1...

commutative properties of four-dimensional generalized symmetric pseudo-riemannian manifolds were considered. specially, in this paper, we studied skew-tsankov and jacobi-tsankov conditions in 4-dimensional pseudo-riemannian generalized symmetric manifolds.

We consider four (real or complex) dimensional hyper-Kähler metrics with a conformal symmetry K. The three-dimensional space of orbits of K is shown to have an Einstein–Weyl structure which admits a shear-free geodesics congruence for which the twist is a constant multiple of the divergence. In this case the Einstein–Weyl equations reduce down to a single second order PDE for one function. The ...

Abstract We construct the propagator of massless Dirac operator W on a closed Riemannian 3-manifold as sum two invariantly defined oscillatory integrals, global in space and time, with distinguished complex-valued phase functions. The integrals—the positive negative propagators—correspond to eigenvalues , respectively. This enables us provide invariant definition full symbols propagators (scala...