2024 B metric manifolds

B metric manifolds

Author: xiaz

August undefined, 2024

WebPGI Manifolds - Parker Hannifin 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 …

Ricci-like solitons on almost contact B-metric manifolds

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 … WebThe 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 douojin

B-METRIC STRUCTURE arXiv:1504.05330v1 [math.DG] …

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 … 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. 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 … radanovic plast

(PDF) Almost contact manifolds with B-metric

WebDec 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 … WebApr 13, 2024 · where $\text {Ric}_g$ denotes the Ricci tensor of g and g runs over all smooth Riemannian metrics on M.They found some topological conditions to ensure that a volume-noncollapsed almost Ricci-flat manifold admits a Ricci-flat metric. By the Cheeger–Gromoll splitting theorem [], any smooth closed Ricci-flat manifold must be … radan sportsWeb2. Almost Contact B-Metric Manifolds, Contact Conformal Transformations, and Yamabe Solitons Let (M, j,x,h, g) be an almost contact manifold with B-metric or an almost contact B-metric manifold, i.e., M is a (2n +1)-dimensional differentiable pseudo-Riemannian manifold with metric g of signature (n +1,n), endowed with an almost contact structure do u oakland

"WebJul 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) " - B metric manifolds

B metric manifolds

Web3. A semisymmetric metric connection on almost contact. B−. metric manifolds In this section we deal with a semisymmetric metric connection on an almost contact. B−. metric manifold. Let (M,φ,ξ,η,g) be an almost contact. B−. metric manifold with the Levi–Civita connection. ∇. g. and we define a semisymmetric connection. ∇. e on ... 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 …

Did you know?

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 ... 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

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 ... WebThere 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 ...

WebAug 5, 2024 · For a given almost contact Norden metric structure on a smooth manifold $ M $, one can obtain an almost complex Norden metric structure on $ M\times\mathbb{R} $. In this work, we study this construction in details and give the relations between the classes of these structures. Furthermore, we give examples of almost … WebJan 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 ...

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 …

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 … radan stojanovicWebDec 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 … radanovoWebDec 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 ... do u ovulate onWebFeb 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 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 … do u ovulate on nexplanonWebAug 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 … doup boj odbojWebFeb 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 … doup gold projectWebOn 5-dimensional almost contact B-metric manifolds, the form of any ϕ-Kähler-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 ϕ-Kähler ... rada obce plat