B metric manifolds
WebA 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 ... 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.
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 … WebOn 5-dimensional almost contact B-metric manifolds, the form of any K\"ahler-type tensor (i.e. a tensor satisfying the properties of the curvature tensor of the Levi-Civita connection in the special class of the parallel structures on the manifold) is determined. The associated 1-forms are derived by the scalar curvatures of the K\" ...
WebNov 20, 2024 · A new class of 3-dimensional contact metric manifolds is found. Moreover it is proved that there are no such manifolds in dimensions greater than 3. Keywords. 53C25 53C15 contact metric manifolds generalized (κ, μ)-contact metric manifolds. Type Research Article. Information WebJan 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 …
WebJun 12, 2024 · A generalization of $\\eta$-Ricci solitons is considered involving an additional metric and functions as soliton coefficients. The soliton potential is torse-forming and orthogonal to the contact distribution of the almost contact B-metric manifold. Then such a manifold can also be considered as an almost Einstein-like manifold, a generalization … 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 9, 2016 · In this paper we study slant null curves with respect to the original parameter on 3-dimensional normal almost contact B-metric manifolds with parallel Reeb vector …
Web33. 1994. A classification of the torsion tensors on almost contact manifolds with B-metric. M Manev, M Ivanova. Central European Journal of Mathematics (Open Mathematics) 12 … ipsum liberty scWebThere are considered 5-dimensional almost contact B-metric manifolds of two basic classes. It is proved that every manifold from the section of these classes is with pointwise constant sectional curvatures. It is studied the curvature tensor of the manifolds of these two classes and some their curvature characteristics are given. Mathematics ... ipsum peoplehrWebJan 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 ... orchard house sawstonWebThe 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 … orchard house romney marshWebDec 20, 2024 · Ricci-like solitons with potential Reeb vector field are introduced and studied on almost contact B-metric manifolds. The cases of Sasaki-like manifolds and torse-forming potentials have been considered. In these cases, it is proved that the manifold admits a Ricci-like soliton if and only if the structure is Einstein-like. Explicit examples of … ipsum laboratoryWebAug 19, 2024 · Ricci-like solitons on Sasaki-like almost contact B-metric manifolds are the object of study. Cases, where the potential of the Ricci-like soliton is the Reeb vector field or pointwise collinear to it, are considered. In the former case, the properties for a parallel or recurrent Ricci-tensor are studied. In the latter case, it is shown that the potential of the … orchard house school dawlishWebJul 4, 2014 · We would like to consider an almost Ricci soliton ( M, g, X, \lambda ) such that g is a K -contact metric and X is a contact vector field. Let us recall that a vector field X on a contact manifold is said to be a contact vector field if. \begin {aligned} \pounds _X \eta = f \eta , \end {aligned} (17) ipsum patent search