On Riemannian tangent bundles.
On some flat connection associated with locally symmetric surface
For every two-dimensional manifold M with locally symmetric linear connection ∇, endowed also with ∇-parallel volume element, we construct a flat connection on some principal fibre bundle P(M,G). Associated with - satisfying some particular conditions - local basis of TM local connection form of such a connection is an R(G)-valued 1-form build from the dual basis ω1, ω2 and from the local connection form ω of ▽. The structural equations of (M,∇) are equivalent to the condition dΩ-Ω∧Ω=0. This work...
On some special vector fields.
On special almost geodesic mappings of type of spaces with affine connection
N. S. Sinyukov [5] introduced the concept of an almost geodesic mapping of a space with an affine connection without torsion onto and found three types: , and . The authors of [1] proved completness of that classification for .By definition, special types of mappings are characterized by equations where is the deformation tensor of affine connections of the spaces and .In this paper geometric objects which preserve these mappings are found and also closed classes of such spaces...
On "special" fibred coordinates for general and classical connections
Using a general connection Γ on a fibred manifold p:Y → M and a torsion free classical linear connection ∇ on M, we distinguish some “special” fibred coordinate systems on Y, and then we construct a general connection on Fp:FY → FM for any vector bundle functor F: ℳ f → of finite order.
On subprojective transformations.
On the Bianchi Identities.
On the Cartan-Norden theorem for affine Kähler immersions
In [O2] the Cartan-Norden theorem for real affine immersions was proved without the non-degeneracy assumption. A similar reasoning applies to the case of affine Kähler immersions with an anti-complex shape operator, which allows us to weaken the assumptions of the theorem given in [NP]. We need only require the immersion to have a non-vanishing type number everywhere on M.
On the connection of recurrence of metric, eigen tensors and transition of length in W-On spaces.
On the extensor structure of a formulation given by W. Ślebodziński
On the functional independence of scalar invariants of curvature for dimensions n=2,3,4
On the Geometry of Affine Immersions.
On the local moduli space of locally homogeneous affine connections in plane domains
Classification of locally homogeneous affine connections in two dimensions is a nontrivial problem. (See [5] and [7] for two different versions of the solution.) Using a basic formula by B. Opozda, [7], we prove that all locally homogeneous torsion-less affine connections defined in open domains of a 2-dimensional manifold depend essentially on at most 4 parameters (see Theorem 2.4).
On the notion of Jacobi fields in constrained calculus of variations
In variational calculus, the minimality of a given functional under arbitrary deformations with fixed end-points is established through an analysis of the so called second variation. In this paper, the argument is examined in the context of constrained variational calculus, assuming piecewise differentiable extremals, commonly referred to as extremaloids. The approach relies on the existence of a fully covariant representation of the second variation of the action functional, based on a family of...
On the reduction formulas
On The Relation Between Connection And Sprays.
On two Tensor Fields Which are Analogous to Curvature and Torsion Tensor Fields
On weakly projective symmetric manifolds.
On weakly symmetric manifolds with a type of semi-symmetric non-metric connection
The object of the present paper is to study weakly symmetric manifolds admitting a type of semi-symmetric non-metric connection.
On Weakly -Symmetric Manifolds
The object of the present paper is to study weakly -symmetric manifolds and its decomposability with the existence of such notions. Among others it is shown that in a decomposable weakly -symmetric manifold both the decompositions are weakly Ricci symmetric.