A note on the volume of $\nabla $-Einstein manifolds with skew-torsion

Ioannis Chrysikos

Displaying similar documents to “A note on the volume of $\nabla $-Einstein manifolds with skew-torsion”

The Srní lectures on non-integrable geometries with torsion

Ilka Agricola (2006)

Archivum Mathematicum

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This review article intends to introduce the reader to non-integrable geometric structures on Riemannian manifolds and invariant metric connections with torsion, and to discuss recent aspects of mathematical physics—in particular superstring theory—where these naturally appear. Connections with skew-symmetric torsion are exhibited as one of the main tools to understand non-integrable geometries. To this aim a a series of key examples is presented and successively dealt with using the...

Distinguished connections on $(J^{2} = \pm 1)$ -metric manifolds

Fernando Etayo, Rafael Santamaría (2016)

Archivum Mathematicum

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We study several linear connections (the first canonical, the Chern, the well adapted, the Levi Civita, the Kobayashi-Nomizu, the Yano, the Bismut and those with totally skew-symmetric torsion) which can be defined on the four geometric types of $(J^{2} = \pm 1)$ -metric manifolds. We characterize when such a connection is adapted to the structure, and obtain a lot of results about coincidence among connections. We prove that the first canonical and the well adapted connections define a one-parameter...

On Uniqueness Theoremsfor Ricci Tensor

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

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

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In Riemannian geometry the prescribed Ricci curvature problem is as follows: given a smooth manifold $M$ and a symmetric 2-tensor $r$ , construct a metric on $M$ whose Ricci tensor equals $r$ . In particular, DeTurck and Koiso proved the following celebrated result: the Ricci curvature uniquely determines the Levi-Civita connection on any compact Einstein manifold with non-negative section curvature. In the present paper we generalize the result of DeTurck and Koiso for a Riemannian manifold with...

New versions of curvature and torsion formulas for the complete lifting of a linear connection to Weil bundles

A. Ntyam, J. Wouafo Kamga (2003)

Annales Polonici Mathematici

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New versions of Slovák’s formulas expressing the covariant derivative and curvature of the linear connection $_{A} Γ$ are presented.

Curvature and torsion formulas for conflict sets

Martijn van Manen (2003)

Banach Center Publications

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Conflict set are the points at equal distance from a number of manifolds. Known results on the differential geometry of these sets are generalized and extended.

Partial integrability on Thurston manifolds

Hyeseon Kim (2013)

Annales Polonici Mathematici

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We determine the maximal number of independent holomorphic functions on the Thurston manifolds $M^{2 r + 2}$ , r ≥ 1, which are the first discovered compact non-Kähler almost Kähler manifolds. We follow the method which involves analyzing the torsion tensor dθ modθ, where $θ = (θ ¹, . . ., θ^{r + 1})$ are independent (1,0)-forms.

How many are equiaffine connections with torsion

Zdeněk Dušek, Oldřich Kowalski (2015)

Archivum Mathematicum

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The question how many real analytic equiaffine connections with arbitrary torsion exist locally on a smooth manifold $M$ of dimension $n$ is studied. The families of general equiaffine connections and with skew-symmetric Ricci tensor, or with symmetric Ricci tensor, respectively, are described in terms of the number of arbitrary functions of $n$ variables.

A classification of the torsion tensors on almost contact manifolds with B-metric

Mancho Manev, Miroslava Ivanova (2014)

Open Mathematics

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The space of the torsion (0,3)-tensors of the linear connections on almost contact manifolds with B-metric is decomposed in 15 orthogonal and invariant subspaces with respect to the action of the structure group. Three known connections, preserving the structure, are characterized regarding this classification.

Webster pseudo-torsion formulas of CR manifolds

Ho Chor Yin (2023)

Archivum Mathematicum

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In this article, we obtain a formula for Webster pseudo-torsion for the link of an isolated singularity of a $n$ -dimensional complex subvariety in $ℂ^{n + 1}$ and we present an alternative proof of the Li-Luk formula for Webster pseudo-torsion for a real hypersurface in $ℂ^{n + 1}$ .

The cuspidal torsion packet on hyperelliptic Fermat quotients

David Grant, Delphy Shaulis (2004)

Journal de Théorie des Nombres de Bordeaux

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Let $ℓ \geq 7$ be a prime, $C$ be the non-singular projective curve defined over $ℚ$ by the affine model $y (1 - y) = x^{ℓ}$ , $\infty$ the point of $C$ at infinity on this model, $J$ the Jacobian of $C$ , and $φ : C \to J$ the albanese embedding with $\infty$ as base point. Let $\bar{ℚ}$ be an algebraic closure of $ℚ$ . Taking care of a case not covered in [], we show that $φ (C) \cap J_{tors} (\bar{ℚ})$ consists only of the image under $φ$ of the Weierstrass points of $C$ and the points $(x, y) = (0, 0)$ and $(0, 1)$ , where $J_{tors}$ denotes the torsion points of $J$ .