B metric manifolds
WebAug 1, 2024 · Almost contact B-metric manifolds. Let us consider an almost contact B-metric manifold denoted by (M, φ, ξ, η, g). This means that M is a (2 n + 1)-dimensional … WebProposition 9.3.2 If M is a Riemannian manifold with metric g, then Mis a metric space with the distance function ddefined above. The metric topology agrees with the manifold topology. Proof. The symmetry of the distance function is immediate, as is its non-negativity. The triangle inequality is also easily established: For any curves γ 1:[a ...
B metric manifolds
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WebDec 18, 2014 · We consider quasi-Einstein metrics in the framework of contact metric manifolds and prove some rigidity results. First, we show that any quasi-Einstein Sasakian metric is Einstein. Next, we prove that any complete K -contact manifold with quasi-Einstein metric is compact Einstein and Sasakian. To this end, we extend these results … WebAlmost contact manifolds with B-metric Let (M, ϕ, ξ, η, g) be an almost contact manifold with B-metric or an almost contact B-metric manifold, i.e. M is a (2n + 1)-dimensional differ- entiable manifold with an almost contact structure (ϕ, ξ, η) consists of an endomorphism ϕ of the tangent bundle, a vector field ξ, its dual 1-form η 1 ...
WebThe metric-affine geometry, founded by E. Cartan, generalizes Riemannian geometry: it uses a metric g and a linear connection ∇ ¯ instead of the Levi-Civita connection ∇ (of … WebJan 12, 2024 · for some 1-form \(\theta \).A Riemannian manifold endowed with such a structure is known as Weyl manifold. Since D is not a metric connection, the Ricci tensor associated with the Weyl connection D is not usually symmetric. Thus, to define an Einstein type equation on Weyl manifold one needs to consider the symmetrized Ricci tensor of …
WebFeb 20, 2024 · A Yamabe soliton is defined on an arbitrary almost-contact B-metric manifold, which is obtained by a contact conformal transformation of the Reeb vector … WebMetric tensor. In the mathematical field of differential geometry, a metric tensor (or simply metric) is an additional structure on a manifold M (such as a surface) that allows defining distances and angles, just as the inner product on a Euclidean space allows defining distances and angles there.
WebDec 20, 2024 · Abstract: Ricci-like solitons with potential Reeb vector field are introduced and studied on almost contact B-metric manifolds. The cases of Sasaki-like manifolds …
Webshow that a 3-dimensional contact metric manifold on which Qφ—φQ is either Sasakian, flat or of constant ξ-sectional curvature k and constant ^-sectional curvature —k. Finally we give some auxiliary results on locally ^-symmetric contact metric 3-manifolds and on contact metric 3-manifolds immersed in a 4-dimensional manifold of contant ... trenery facebookWebmost contact B-metric structure generated by the pair of associated B-metrics and their Levi-Civita connections. By means of the constructed non-symmetric connections, the … temps today near meWebDec 20, 2024 · An almost c ontact B-metric manifold (M, ϕ, ξ, η , g) is c al led a Ricci-like solito n with potential vecto r field ξ if its Ricci tensor ρ satisfies the fol lowing condition for a triplet ... temps today staffingWebJan 1, 1993 · We consider almost contact B-metric manifolds denoted by (M, ϕ, ξ, η, ). This means that any M is a (2n + 1)-dimensional smooth manifold equipped with an … trenery farm cornwallWebJan 1, 1993 · An example of an F 5 -manifold as an isotropic hypersurface with respect to the associated B-metric in an evendimensional real space is given in [8] and it is noted that the class F 5 is analogous ... temps today ukWebA Yamabe soliton is defined on an arbitrary almost-contact B-metric manifold, which is obtained by a contact conformal transformation of the Reeb vector field, its dual contact 1-form, the B-metric, and its associated B-metric. The cases when the given manifold is cosymplectic or Sasaki-like are studied. In this manner, manifolds are obtained ... temps toeicWebThe standard Euclidean metric on Rn,namely, g = dx2 1 +···+dx2 n, makes Rn into a Riemannian manifold. Then, every submanifold, M,ofRn inherits a metric by restricting the Euclidean metric to M. For example, the sphere, Sn1,inheritsametricthat makes Sn1 into a Riemannian manifold. It is instructive to find the local expression of this metric temp stockton ca