Displaying similar documents to “Complete Riemannian manifolds admitting a pair of Einstein-Weyl structures”

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.

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.

Three dimensional near-horizon metrics that are Einstein-Weyl

Matthew Randall (2017)

Archivum Mathematicum

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We investigate which three dimensional near-horizon metrics g N H admit a compatible 1-form X such that ( X , [ g N H ] ) defines an Einstein-Weyl structure. We find explicit examples and see that some of the solutions give rise to Einstein-Weyl structures of dispersionless KP type and dispersionless Hirota (aka hyperCR) type.

A characterization of the Riemann extension in terms of harmonicity

Cornelia-Livia Bejan, Şemsi Eken (2017)

Czechoslovak Mathematical Journal

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If ( M , ) is a manifold with a symmetric linear connection, then T * M can be endowed with the natural Riemann extension g ¯ (O. Kowalski and M. Sekizawa (2011), M. Sekizawa (1987)). Here we continue to study the harmonicity with respect to g ¯ initiated by C. L. Bejan and O. Kowalski (2015). More precisely, we first construct a canonical almost para-complex structure 𝒫 on ( T * M , g ¯ ) and prove that 𝒫 is harmonic (in the sense of E. García-Río, L. Vanhecke and M. E. Vázquez-Abal (1997)) if and only if g ¯ reduces...

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...

The natural transformations between r-tangent and r-cotangent bundles over Riemannian manifolds

Jan Kurek, Włodzimierz Mikulski (2014)

Annales Universitatis Mariae Curie-Sklodowska, sectio A – Mathematica

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If ( M , g ) is a Riemannian manifold, we have the well-known base preserving   vector bundle isomorphism T M = ˜ T * M given by v g ( v , - ) between the tangent T M and the cotangent T * M bundles of M . In the present note, we generalize this isomorphism to the one T ( r ) M = ˜ T r * M between the r -th order vector tangent T ( r ) M = ( J r ( M , R ) 0 ) * and the r -th order cotangent T r * M = J r ( M , R ) 0 bundles of M . Next, we describe all base preserving  vector bundle maps C M ( g ) : T ( r ) M T r * M depending on a Riemannian metric g in terms of natural (in g ) tensor fields on M .

On the multiplicity of eigenvalues of conformally covariant operators

Yaiza Canzani (2014)

Annales de l’institut Fourier

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Let ( M , g ) be a compact Riemannian manifold and P g an elliptic, formally self-adjoint, conformally covariant operator of order m acting on smooth sections of a bundle over M . We prove that if P g has no rigid eigenspaces (see Definition 2.2), the set of functions f C ( M , ) for which P e f g has only simple non-zero eigenvalues is a residual set in C ( M , ) . As a consequence we prove that if P g has no rigid eigenspaces for a dense set of metrics, then all non-zero eigenvalues are simple for a residual set of metrics...

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 .

Conformal harmonic forms, Branson–Gover operators and Dirichlet problem at infinity

Erwann Aubry, Colin Guillarmou (2011)

Journal of the European Mathematical Society

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For odd-dimensional Poincaré–Einstein manifolds ( X n + 1 , g ) , we study the set of harmonic k -forms (for k < n / 2 ) which are C m (with m ) on the conformal compactification X ¯ of X . This set is infinite-dimensional for small m but it becomes finite-dimensional if m is large enough, and in one-to-one correspondence with the direct sum of the relative cohomology H k ( X ¯ , X ¯ ) and the kernel of the Branson–Gover [3] differential operators ( L k , G k ) on the conformal infinity ( X ¯ , [ h 0 ] ) . We also relate the set of C n - 2 k + 1 ( Λ k ( X ¯ ) ) forms in the kernel of d + δ g ...

On the Picard number of divisors in Fano manifolds

Cinzia Casagrande (2012)

Annales scientifiques de l'École Normale Supérieure

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Let  X be a complex Fano manifold of arbitrary dimension, and D a prime divisor in  X . We consider the image 𝒩 1 ( D , X ) of  𝒩 1 ( D ) in  𝒩 1 ( X ) under the natural push-forward of 1 -cycles. We show that ρ X - ρ D codim 𝒩 1 ( D , X ) 8 . Moreover if codim 𝒩 1 ( D , X ) 3 , then either X S × T where S is a Del Pezzo surface, or codim 𝒩 1 ( D , X ) = 3 and X has a fibration in Del Pezzo surfaces onto a Fano manifold T such that ρ X - ρ T = 4 .

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 G -sets and isospectrality

Ori Parzanchevski (2013)

Annales de l’institut Fourier

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We study finite G -sets and their tensor product with Riemannian manifolds, and obtain results on isospectral quotients and covers. In particular, we show the following: If M is a compact connected Riemannian manifold (or orbifold) whose fundamental group has a finite non-cyclic quotient, then M has isospectral non-isometric covers.