In a previous article it was proved that the extensions of the TaubNUT geometry do not admit Killing-Yano tensors, even if they possess Stäckel-Killing tensors. Here the analysis is taken further, and it is shown that, in general, this class of metrics does not even admit fsymbols. The only exception is the original Taub-NUT metric which possesses four Killing-Yano tensors of valence two. 1 Ext...

In a previous article it was proved that the extensions of the TaubNUT geometry do not admit Killing-Yano tensors, even if they possess Stäckel-Killing tensors. Here the analysis is taken further, and it is shown that, in general, this class of metrics does not even admit fsymbols. The only exception is the original Taub-NUT metric which possesses four Killing-Yano tensors of valence two. 1 Ext...

We demonstrate the use of several tools from Algebraic Combinatorics such as Young tableaux, symmetry operators, the Littlewood-Richardson rule and discrete Fourier transforms of symmetric groups in investigations of algebraic curvature tensors. In [10, 12, 13] we constructed and investigated generators of algebraic curvature tensors and algebraic covariant derivative curvature tensors. These i...

We show that the symmetry classes of torsion-free covariant derivatives ∇T of r-times covariant tensor fields T can be characterized by LittlewoodRichardson products σ[1] where σ is a representation of the symmetric group Sr which is connected with the symmetry class of T . If σ ∼ [λ] is irreducible then σ[1] has a multiplicity free reduction [λ][1] ∼ ∑ λ⊂μ[μ] and all primitive idempotents belo...

in order to study the effect of elevation on quantitative and qualitative characteristics of the humid forests of guilan shafaroud, series 17, 16 and 7 were selected that fall in to three height classes; class 1 (‏less than 500 m), class 2 (‏500 – 1000 m) and class 3 (‏1000 – 1600 m). in height class 1, 2 and 3 sample plots were determined as 4, 15 and 20 respectively and each sample plot was 0...