Displaying similar documents to “On a Semi-symmetric Metric Connection in an Almost Kenmotsu Manifold with Nullity Distributions”

Singer-Thorpe bases for special Einstein curvature tensors in dimension 4

Zdeněk Dušek (2015)

Czechoslovak Mathematical Journal

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Let ( M , g ) be a 4-dimensional Einstein Riemannian manifold. At each point p of M , the tangent space admits a so-called Singer-Thorpe basis (ST basis) with respect to the curvature tensor R at p . In this basis, up to standard symmetries and antisymmetries, just 5 components of the curvature tensor R are nonzero. For the space of constant curvature, the group O ( 4 ) acts as a transformation group between ST bases at T p M and for the so-called 2-stein curvature tensors, the group Sp ( 1 ) SO ( 4 ) acts as a transformation...

Approximately Einstein ACH metrics, volume renormalization, and an invariant for contact manifolds

Neil Seshadri (2009)

Bulletin de la Société Mathématique de France

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To any smooth compact manifold M endowed with a contact structure H and partially integrable almost CR structure J , we prove the existence and uniqueness, modulo high-order error terms and diffeomorphism action, of an approximately Einstein ACH (asymptotically complex hyperbolic) metric g on M × ( - 1 , 0 ) . We consider the asymptotic expansion, in powers of a special defining function, of the volume of M × ( - 1 , 0 ) with respect to g and prove that the log term coefficient is independent of J (and any choice...

η -Ricci Solitons on η -Einstein ( L C S ) n -Manifolds

Shyamal Kumar Hui, Debabrata Chakraborty (2016)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

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The object of the present paper is to study η -Ricci solitons on η -Einstein ( L C S ) n -manifolds. It is shown that if ξ is a recurrent torse forming η -Ricci soliton on an η -Einstein ( L C S ) n -manifold then ξ is (i) concurrent and (ii) Killing vector field.

Some type of semisymmetry on two classes of almost Kenmotsu manifolds

Dibakar Dey, Pradip Majhi (2021)

Communications in Mathematics

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The object of the present paper is to study some types of semisymmetry conditions on two classes of almost Kenmotsu manifolds. It is shown that a ( k , μ ) -almost Kenmotsu manifold satisfying the curvature condition Q · R = 0 is locally isometric to the hyperbolic space 2 n + 1 ( - 1 ) . Also in ( k , μ ) -almost Kenmotsu manifolds the following conditions: (1) local symmetry ( R = 0 ) , (2) semisymmetry ( R · R = 0 ) , (3) Q ( S , R ) = 0 , (4) R · R = Q ( S , R ) , (5) locally isometric to the hyperbolic space 2 n + 1 ( - 1 ) are equivalent. Further, it is proved that a ( k , μ ) ' -almost Kenmotsu manifold...

The Killing Tensors on an n -dimensional Manifold with S L ( n , ) -structure

Sergey E. Stepanov, Irina I. Tsyganok, Marina B. Khripunova (2016)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

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In this paper we solve the problem of finding integrals of equations determining the Killing tensors on an n -dimensional differentiable manifold M endowed with an equiaffine S L ( n , ) -structure and discuss possible applications of obtained results in Riemannian geometry.

Complete Riemannian manifolds admitting a pair of Einstein-Weyl structures

Amalendu Ghosh (2016)

Mathematica Bohemica

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We prove that a connected Riemannian manifold admitting a pair of non-trivial Einstein-Weyl structures ( g , ± ω ) with constant scalar curvature is either Einstein, or the dual field of ω is Killing. Next, let ( M n , g ) be a complete and connected Riemannian manifold of dimension at least 3 admitting a pair of Einstein-Weyl structures ( g , ± ω ) . Then the Einstein-Weyl vector field E (dual to the 1 -form ω ) generates an infinitesimal harmonic transformation if and only if E is Killing.

Some Classes of Lorentzian α -Sasakian Manifolds Admitting a Quarter-symmetric Metric Connection

Santu DEY, Buddhadev Pal, Arindam BHATTACHARYYA (2016)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

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The object of the present paper is to study a quarter-symmetric metric connection in an Lorentzian α -Sasakian manifold. We study some curvature properties of an Lorentzian α -Sasakian manifold with respect to the quarter-symmetric metric connection. We study locally φ -symmetric, φ -symmetric, locally projective φ -symmetric, ξ -projectively flat Lorentzian α -Sasakian manifold with respect to the quarter-symmetric metric connection.

A universal bound for lower Neumann eigenvalues of the Laplacian

Wei Lu, Jing Mao, Chuanxi Wu (2020)

Czechoslovak Mathematical Journal

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Let M be an n -dimensional ( n 2 ) simply connected Hadamard manifold. If the radial Ricci curvature of M is bounded from below by ( n - 1 ) k ( t ) with respect to some point p M , where t = d ( · , p ) is the Riemannian distance on M to p , k ( t ) is a nonpositive continuous function on ( 0 , ) , then the first n nonzero Neumann eigenvalues of the Laplacian on the geodesic ball B ( p , l ) , with center p and radius 0 < l < , satisfy 1 μ 1 + 1 μ 2 + + 1 μ n l n + 2 ( n + 2 ) 0 l f n - 1 ( t ) d t , where f ( t ) is the solution to f ' ' ( t ) + k ( t ) f ( t ) = 0 on ( 0 , ) , f ( 0 ) = 0 , f ' ( 0 ) = 1 .

The vertical prolongation of the projectable connections

Anna Bednarska (2012)

Annales Universitatis Mariae Curie-Sklodowska, sectio A – Mathematica

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We prove that any first order 2 m 1 , m 2 , n 1 , n 2 -natural operator transforming projectable general connections on an ( m 1 , m 2 , n 1 , n 2 ) -dimensional fibred-fibred manifold p = ( p , p ) : ( p Y : Y Y ) ( p M : M M ) into general connections on the vertical prolongation V Y M of p : Y M is the restriction of the (rather well-known) vertical prolongation operator 𝒱 lifting general connections Γ ¯ on a fibred manifold Y M into 𝒱 Γ ¯ (the vertical prolongation of Γ ¯ ) on V Y M .

On canonical constructions on connections

Jan Kurek, Włodzimierz Mikulski (2016)

Annales Universitatis Mariae Curie-Sklodowska, sectio A – Mathematica

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We study  how a projectable general connection Γ in a 2-fibred manifold Y 2 Y 1 Y 0   and a general vertical connection Θ in Y 2 Y 1 Y 0 induce a general connection A ( Γ , Θ ) in Y 2 Y 1 .

Tensor products of higher almost split sequences in subcategories

Xiaojian Lu, Deren Luo (2023)

Czechoslovak Mathematical Journal

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We introduce the algebras satisfying the ( , n ) condition. If Λ , Γ are algebras satisfying the ( , n ) , ( , m ) condition, respectively, we give a construction of ( m + n ) -almost split sequences in some subcategories ( ) ( i 0 , j 0 ) of mod ( Λ Γ ) by tensor products and mapping cones. Moreover, we prove that the tensor product algebra Λ Γ satisfies the ( ( ) ( i 0 , j 0 ) , n + m ) condition for some integers i 0 , j 0 ; this construction unifies and extends the work of A. Pasquali (2017), (2019).