Abstract
The derivation formulae of the vector fields of an arbitrary net belonging to the n-dimensional equiaffine spaceEqA n are introduced and the conditions which satisty their coefficients are found. The following special nets: Chebyshev of the first and second kind, strongly parallel of the first kind, geodesic, generalized metrical Chebyshev and symmetric nets are studied. Their characteristics by the coefficients of the derivation equations are obtained. Chebyshev and geodesic curvatures of the lines of the net belonging toEqA n and Chebyshev and geodesic vectors of the nets are introduced. Equiaffine spaces containing above mention special nets are defined.
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The present investigation is partially supported by the Nacional Science Fund of the Ministry of Science and Education, Republic of Bulgaria under grant MM 64.
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Zlatanov, G., Tsareva, B. Geometry of the nets in equiaffine spaces. J Geom 55, 192–201 (1996). https://doi.org/10.1007/BF01223045
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DOI: https://doi.org/10.1007/BF01223045