Finsleroid -- space supplemented by angle and scalar product
2004jav | Asanov G. S.

The science of the past century has achieved great success on the basis of the geometrical quadratic concepts that were followed as logical and mathematical primaries. More profound ideas will imply using a more capacious class of geometries, for example the Finsler one which inscribes structures because the Finslerian indicatrices are no more isotropic in all directions. In the present work an attempt is made to resolve the respective difficulties of Finsler generalization by choosing the particular Finsleroid--type metric that implies one preferred direction, admitting the total axial symmetry around it. In this case, interesting constructive methods of introducing the concept of the angle and scalar product outside the frame of the Euclidean Geometry can conveniently be opened up.

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