A note on Poisson-Lie algebroids. I.
A note on the volume of -Einstein manifolds with skew-torsion
We study the volume of compact Riemannian manifolds which are Einstein with respect to a metric connection with (parallel) skew-torsion. We provide a result for the sign of the first variation of the volume in terms of the corresponding scalar curvature. This generalizes a result of M. Ville [Vil] related with the first variation of the volume on a compact Einstein manifold.
A pseudo-Riemannian metric on the tangent bundle of a Riemannian manifold.
A remark on semi-∇-flat functions
We give a pointwise characterization of semi-∇-flat functions on an affine manifold (M,∇).
A remarkable transformation group on cotangent bundle.
Affine Anosov diffeomorphims of affine manifolds.
Affine connections on almost para-cosymplectic manifolds
Identities for the curvature tensor of the Levi-Cività connection on an almost para-cosymplectic manifold are proved. Elements of harmonic theory for almost product structures are given and a Bochner-type formula for the leaves of the canonical foliation is established.
Affine Structures on Compact Complex Manifolds.
Affinoid structures and connections
Algèbres de Maurer-Cartan et Holonomie
Almost pseudo symmetric Sasakian manifold admitting a type of quarter symmetric metric connection
In the present paper we have obtained the necessary condition for the existence of almost pseudo symmetric and almost pseudo Ricci symmetric Sasakian manifold admitting a type of quarter symmetric metric connection.
Almost symplectic -linear connections in the bundle of accelerations.
An anti-Kählerian Einstein structure on the tangent bundle of a space form
In [11] we have considered a family of almost anti-Hermitian structures (G,J) on the tangent bundle TM of a Riemannian manifold (M,g), where the almost complex structure J is a natural lift of g to TM interchanging the vertical and horizontal distributions VTM and HTM and the metric G is a natural lift of g of Sasaki type, with the property of being anti-Hermitian with respect to J. Next, we have studied the conditions under which (TM,G,J) belongs to one of the eight classes of anti-Hermitian structures...
An -isolation theorem for Yang-Mills fields over complete manifolds
Analysis in complex quaternions and its connections with mathematical physics
Automorphisms of Spacetime Manifold with Torsion
In this paper we prove that the maximum dimension of the Lie group of automorphisms of the Riemann–Cartan 4-dimensional manifold does not exceed 8, and if the Cartan connection is skew-symmetric or semisymmetric, the maximum dimension is equal to 7. In addition, in the case of the Riemann–Cartan -dimensional manifolds with semisymmetric connection the maximum dimension of the Lie group of automorphisms is equal to for any .