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ABSTRACT: M. Matsumoto in his paper [1-2] obtained the equations of geodesic in a two-dimensional
Randers, Kropina and Matsumoto space. In the present paper we have found out the
equation of geodesic for a more general α, β-metric as compared to Randers, Kropina and Matsumoto mertric.
Hypercomplex Numbers in Geometry and Physics. 01/2011; 8:143-150.
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ABSTRACT: M. Matsumoto introduced the concept of (α,β)-metric in the year, 1972. In the present paper we have the concept of
generalized (α,β)-metric by taking L(α,β^(1)),β^(2)),…….,β^(m))) as homogeneous function of degree one in α,
β^(1)),β^(2)),…….,β^(m))where α=√(a_ij (x)y^i y^j ) is a purely Riemannian metric and〖 β〗^(1)),β^(2)),…….,β^(m)) all are one-form. In
the present paper we have found out the main scalar I of two-dimensional Finsler space with generalized (α,β)-
metric..
BPAM. 01/2010; 4(2):168-177.
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ABSTRACT: In the present paper we have obtain scalar curvature R of Two-dimensional Finsler space with (α,β)-metric. Some
special (α,β)-metric such as Randers metric, Kropina metric, Generalized Kropina metric and Matsumoto metric have
also been considered and explicit expression for scalar curvature R has been find out.
Ganita. 01/2009; 60:9-14.
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ABSTRACT: The (α,β)-metric is a Finsler metric which is constructed from a Riemannian metric α and a differential one-form β,
and has been sometimes treated in theoretical physics. In 1995, M. Kitayama, M. Azuma and M. Matsumoto found
out the main scalars with (α,β)-metric. The purpose of the present paper is to find out main scalars H, I, J in three-
dimensional Finsler space with (α,β)-metric, and some special (α,β)-metric has also been dealt
ABM. 01/2009; 28:51-55.
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ABSTRACT: The theory of m-th root metrics has been first developed by H. Shimada as an interesting example of Finsler metrics, immediately following M. Matsumoto and S. Numata’s theory of cubic metrics. By introducing the regularity of the metric various fundamental quantities as a Finsler metric could be found. In particular, the Cartan connection of a Finsler space with m-th root metric could be discussed from the theoretical standpoint. M. Matsumoto and K. Okubo studied Berwald connection of Finsler spaces with m-th root metric and give main scalars in two-dimensional case,
and also defined higher order Christoffel symbols. In the present paper we have worked out the non-linear connection of Berwald and Cartan connection of a Finsler space with m-th root metric. Furthermore, we also find out main scalars of m-th root metric, in particular, of cubic and quartic metrics of a three-dimensional Finsler space.
JIAOPS. 01/2008; 12:139-150.
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ABSTRACT: In Two-dimensional Finsler space F2 the main scalar I and curvature R have important roles. The purpose of the present paper is to obtain scalar curvature R of Two-dimensional Finsler space with cubic metric. Some special cubic metric have been considered and explicit expression for scalar curvature R has been found as given in equations (3.2), (3.3). Variation of scalar curvature has been plotted in figure.
JIAOPS. 01/2008; 12:127-137.
