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Equipping distributions for linear distribution

Marina F. Grebenyuk, Josef Mikeš (2007)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

In this paper there are discussed the three-component distributions of affine space A n + 1 . Functions { σ } , which are introduced in the neighborhood of the second order, determine the normal of the first kind of -distribution in every center of -distribution. There are discussed too normals { 𝒵 σ } and quasi-tensor of the second order { 𝒮 σ } . In the same way bunches of the projective normals of the first kind of the -distributions were determined in the differential neighborhood of the second and third order.

Infinitesimal bending of a subspace of a space with non-symmetric basic tensor

Svetislav M. Minčić, Ljubica S. Velimirović (2005)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

In this work infinitesimal bending of a subspace of a generalized Riemannian space (with non-symmetric basic tensor) are studied. Based on non-symmetry of the connection, it is possible to define four kinds of covariant derivative of a tensor. We have obtained derivation formulas of the infinitesimal bending field and integrability conditions of these formulas (equations).

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