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On $(N(k),ξ)$-semi-Riemannian manifolds: Semisymmetries
(N(k), ξ)-semi-Riemannian manifold T -curvature tensor quasi-conformal curvature tensor
2012/2/29
$(N(k),\xi)$-semi-Riemannian manifolds are defined. Examples and properties of $(N(k),\xi)$-semi-Riemannian manifolds are given. Some relations involving ${\cal T}_{a}$-curvature tensor in $(N(k),\xi)...
Sub-Riemannian structures corresponding to K鋒lerian metrics on the universal Teichmueller space and curve
Teichmuller space group of diffeomorphisms Lie-Frechet group Virasoro-Bott group Virasoro algebra sub-Riemannian geometry
2012/2/29
We consider the group of sense-preserving diffeomorphisms $\Diff S^1$ of the unit circle and its central extension, the Virasoro-Bott group, with their respective horizontal distributions chosen to be...
Para-CR Structures on almost Paracontact Metric Manifolds
Para-CR manifolds para-Sasakian manifolds almost paracontact metric manifolds paracontact metric manifolds
2012/3/1
Almost paracontact metric manifolds are the famous examples of almost para-CR manifolds. We find necessary and suffcient conditions for such manifolds for be para-CR. Next we examine these conditions ...
Yang-Mills connections of cohomogeneity one on SO(n)-bundles over Euclidean spheres
Yang-Mills connections of cohomogeneity one SO(n)-bundles Euclidean spheres Differential Geometry
2011/9/23
Abstract: We construct Yang-Mills connections on SO(n)-bundles over spheres equipped with the Euclidean metric. We use a cohomogeneity one group action on the bundle to reduce the Yang-Mills-equation ...
Goryachev-Chaplygin, Kovalevskaya, and Brdicka-Eardley-Nappi-Witten pp-waves spacetimes with higher rank Stackel-Killing tensors
Goryachev-Chaplygin Kovalevskaya Brdicka-Eardley-Nappi-Witten pp-waves spacetimes Differential Geometry
2011/10/10
Abstract: Hidden symmetries of the Goryachev-Chaplygin and Kovalevskaya gyrostats spacetimes, as well as the Brdi\v{c}ka-Eardley-Nappi-Witten pp-waves are studied. We find out that these spacetimes po...
Inegalite de Sobolev et volume asymptotique
Sobolev inequality volume growth locally conformally flat
2011/9/23
Abstract: A result of M. Ledoux is that a complete Riemannian manifold with non negative Ricci curvature satisfying the Euclidean Sobolev inequality is the Euclidean space. We present a shortcut of th...
On prolongations of contact manifolds
prolongations of contact manifolds Symplectic Geometry Differential Geometry
2011/9/23
Abstract: In this note, we apply spectral sequences to both derive an obstruction to the existence of $n$-fold prolongations and to derive a topological classification. Prolongations were formerly use...
Higher Symmetries of the Laplacian via Quantization
Symmetry algebra Laplacian Quantization Conformal geometry Minimal nilpotent orbit
2011/9/22
Abstract: We develop a new approach, based on quantization methods, to study higher symmetries of invariant differential operators. We focus here on conformally invariant powers of the Laplacian over ...
Parallel submanifolds of the real 2-Grassmannian
Parallel submanifolds real 2-Grassmannian Differential Geometry
2011/9/22
Abstract: We classify parallel submanifolds of the Grassmannian $\rmG^+_2(\R^{n+2})$ which parameterizes the oriented 2-planes of the Euclidean space $\R^{n+2}$. Our main result states that every comp...
The Intrinsic Geometry of Almost Contact Metric Manifolds
almost contact manifold Sasakian manifold K-contact manifold the intrinsic geometry of almost contact metric manifolds
2011/9/22
Abstract: In this paper the notion of the intrinsic geometry of an almost contact metric manifold is introduced. Description of some classes of spaces with almost contact metric structures in terms of...
Abstract: We study variations of the G_2 structure on the unit tangent sphere bundle, introduced in [Alb2,AlbSal1,AlbSal2] and now called gwistor space. We analize the equations of calibration and coc...
On the characteristic torsion of gwistor space
Einstein metric gwistor space characteristic torsion G2 structure
2011/9/21
Abstract: We give a presentation of gwistor space. Then we compute the characteristic torsion T^ch of the G_2-twistor space of an oriented Riemannian 4-manifold with constant sectional curvature k and...
Curvatures of weighted metrics on tangent sphere bundles
metric connection tangent sphere bundle curvature
2011/9/21
Abstract: We determine the curvature equations of natural metrics on tangent bundles and radius r tangent sphere bundles S_rM of a Riemannian manifold M. A family of positive scalar curvature metrics ...
Splitting of 3-Manifolds and Rigidity of Area-Minimising Surfaces
Rigidity of Area-Minimising Surfaces Splitting of 3-Manifolds Differential Geometry
2011/9/21
Abstract: In this paper we prove an area comparison result for certain totally geodesic surfaces in 3-manifolds with a lower bound on the scalar curvature. This result is a variant of a comparison the...
Bifurcation and local rigidity of homogeneous solutions to the Yamabe problem on spheres
homogeneous solutions Yamabe problem spheres Differential Geometry
2011/9/21
Abstract: We study existence and non existence of constant scalar curvature metrics conformal and arbitrarily close to homogeneous metrics on spheres, using variational techniques. This describes all ...