Mathematics – Differential Geometry
Scientific paper
2011-09-13
Mathematics
Differential Geometry
Scientific paper
The Finsler spaces in which the tangent Riemannian spaces are conformally flat prove to be characterized by the condition that the indicatrix is a space of constant curvature. In such spaces the Finslerian normalized two-vector angle can be explicated from the respective two-vector angle of the associated Riemannian space. Therefore the way is opening to propose explicitly the connection preserving the angle even at the indicatrix-inhomogeneous level, that is, when the indicatrix curvature value ${\mathcal C}_{\text{Ind.}} $ is permitted to be an arbitrary smooth function of the indicatrix position point $x$. The connection obtained is metrical with the deflection part which is proportional to the gradient of the function $H(x)$ entering the equality ${\mathcal C}_{\text{Ind.}} \equiv H^2.$ Also the connection is covariant-constant. When the transitivity of covariant derivative is used, from the commutators of covariant derivatives the associated curvature tensor is found. Various useful representations have been developed. The Finsleroid space has been explicitly outlined.
No associations
LandOfFree
Finsler connection preserving the two-vector angle under the indicatrix-inhomogeneous treatment does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Finsler connection preserving the two-vector angle under the indicatrix-inhomogeneous treatment, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Finsler connection preserving the two-vector angle under the indicatrix-inhomogeneous treatment will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-333052