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001-es BibID:	BIBFORM099423
Első szerző:	Tamássy Lajos (matematikus)
Cím:	Finsler geometry in the tangent bundle / Lajos Tamássy
Dátum:	2007
Megjegyzések:	Linear and metrical connections of a Riemannian space, whose indicatrices are ellipsoids, are established in the tangent bundle. lndicatrices of Finsler spaces are smooth, starshaped and convex hypersurfaces. They do not transform, in general, into each other by linear transformations, and thus they do not admit linear metrical connections in the tangent bundle. This necessitates the introduction of lineelements yielding the dependence of the geometric objects not only of points x but also of the direction y. Therefore, the apparatus (connections, covariant derivatives, curvatures, etc.) of Finsler geometry becomes inevitably a little more complicated. Nevertheless there are a number of problems which need no lineelements. Such are those, which concern the metric only (arc length, area, angle, geodesics, etc.) and also the investigation of those important special Finsler spaces, which allow linear metrical connections in the tangent bundle. In this paper we want to present results which use the tangent bundle T M only, and do not need TTA1 or VT AI or line-elements. These investigations often admit direct geometrical considerations. Longer proofs are only sketched or omitted.
ISBN:	9784931469426
Tárgyszavak:	Természettudományok Matematika- és számítástudományok könyvfejezet könyvrészlet distance in Finsler spaces Minkowski-Finsler angle deviation from Riemann spaces locally Minkowski spaces connections in the tangent bundle
Megjelenés:	Finsler Geometry, Sapporo 2005 : In memory of Makoto Matsumoto / ed. Sorin V. Sabau, Hideo Shimada. - p. 163-194. -
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