B metric manifolds

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August undefined, 2024

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 ... WebAug 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 …

Curvature Properties on Some Classes of Almost Contact Manifolds with B ...

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 ... 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 … knee high slippers australia

Yamabe solitons on conformal Sasaki-like almost contact B-metric manifolds

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. 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 ... WebMar 30, 2024 · We prove that a Kähler B-metric manifold is of constant totally real sectional curvatures if and only if it is a holomorphic Einstein, Bochner flat manifold. We also find the necessary and sufficient conditions for a gradient Ricci soliton or a holomorphic η-Einstein Kähler B-metric manifold to be Bochner flat. In this context, the manifolds ... red book medication costs

Yamabe Solitons on Some Conformal Almost Contact B-Metric Manifolds

(PDF) Almost contact manifolds with B-metric

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 … 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 ... knee high slippers red book maternity

"Web2. 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 " - B metric manifolds

B metric manifolds

$Almost Ricci solitons and $K$ -contact geometry - Springer$

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) 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 …

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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 ... 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 …

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 … 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 …

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 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 ...

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 …

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 … red book marriottWebApr 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 … red book michiganWebDec 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 … knee high slouch boots flatWebPGI Manifolds - Parker Hannifin knee high slouch bootsWebDec 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 ... red book maoWebOn 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\" ... red book milestonesWebThe 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 knee high slipper socks for women grippers