We show how the ad hoc prescriptions appearing in 2001 for the Lie derivative of Lorentz tensors are a direct consequence of the Kosmann lift defined earlier, in a much more general setting encompassing older results of Y. Kosmann about Lie derivatives of spinors.
The aim of this paper is to investigate the orthogonality of vectors to each other and the Gram-Schmidt method in the Minkowski space . Hyperbolic cosine formulas are given for all triangle types in the Minkowski plane . Moreover, the Pedoe inequality is explained for each type of triangle with the help of hyperbolic cosine formulas. Thus, the Pedoe inequality allowed us to establish a connection between two similar triangles in the Minkowski plane. In the continuation of the study, the rotation...
The article deals with bundles of linear algebra as a specifications of the case of smooth manifold. It allows to introduce on smooth manifold a metric by a natural way. The transfer of geometric structure arising in the linear spaces of associative algebras to a smooth manifold is also presented.
We describe conditions under which a spacetime connection and a scaled Lorentzian metric define natural symplectic and Poisson structures on the tangent bundle of the Einstein spacetime.
The article deals with spaces the geometry of which is defined by cyclic and anticyclic algebras. Arbitrary multiplicative function is taken as a fundamental form. Motions are given as linear transformation preserving given multiplicative function.
In this paper we consider holomorphically projective mappings from the compact semisymmetric spaces onto (pseudo-) Kählerian spaces . We proved that in this case space is holomorphically projective flat and is space with constant holomorphic curvature. These results are the generalization of results by T. Sakaguchi, J. Mikeš, V. V. Domashev, N. S. Sinyukov, E. N. Sinyukova, M. Škodová, which were done for holomorphically projective mappings of symmetric, recurrent and semisymmetric Kählerian...
The article is devoted to a generalization of Clifford and Grassmann algebras for the case of vector spaces over the field of complex numbers. The geometric interpretation of such generalizations are presented. Multieuclidean geometry is considered as well as the importance of it in physics.
In this paper, we study closed -maximal spacelike hypersurfaces in anti-de Sitter space with two distinct principal curvatures and give some integral formulas about these hypersurfaces.