We may use geodesic-arc angle to construct the geodesic-arc sector S{x} (l1 , l2 ) ⊂ TxM , where l1 , l2 ∈ TxM are two unit vectors issued from the origin 0 ∈ TxM (and pointed to the indicatrix).
Finsleroid gives rise to the angle-preserving connection
RN and h2(x) is the value of curvature of the indicatrix supported by point x (see (2.6)).
Finsleroid gives rise to the angle-preserving connection
At each point x ∈ M , the ratio AREAFinsleroid Indicatrix /V OLU M EFinsleroid proves to be of the universal value in each dimension N (is independent of h), so that the ratio is exactly the same as it holds in the Riemannian limit (that is, when h = 1).
Finsleroid gives rise to the angle-preserving connection
However, there exists a simple possibility to elucidate the global structure of the F F P D -Finsleroid indicatrix.
Finsleroid gives rise to the angle-preserving connection
The equality (3.7) manifests that the transformation (6.26) maps -Finsleroid indicatrix in regions of the sphere S {ζ } regions of the F F P D {x} .
Finsleroid gives rise to the angle-preserving connection
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