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The purpose of this paper is to examine the condition for a Finsler space with a generalized α , β -metric to be projectively flat. In addition, we establish that the Finsler space with generalized α , β -metric is a flat-parallel Minkowski space and derive the condition under which the β -change for the aforementioned metric is projective. We also explored the projective nature of β -change for various significant Finsler metrics derived from the generalized α , β -metric. [ABSTRACT FROM AUTHOR]

In the present paper, we study the Finslerian hypersurfaces of a special generalized (α, β)-metric in the form L(α, β) = α(β α), with condition (0) = 0 (0) = 00 (0) = 000 (0) = 1. Further, we examined the hypersurfaces of this special metric as a hyperplane of first, second and third kinds with certain condition on the above Finsler metric. [ABSTRACT FROM AUTHOR]

R. Miron initiated the study of L-duality in Lagrange and Finsler spaces in 1987. The concrete L-duals of the Randers metric, Kropina metric, Matsumoto metric, exponential metric, as well as a few more unique (a, B)- metrics, are really just an of the remarkable results obtained. The importance of L-duality, however, is basically limited to finding the dual of a few key Finsler functions. In this paper, we find L- Dual of a Finsler space with a special (a, B)- metric F =, where a is a Riemannian metric and B is a differential one form. [ABSTRACT FROM AUTHOR]

In 1997, S. Basco and M. Matsumoto introduced the concepts of Douglas spaces with a generalization of the notion of Berwald spaces. Weakly-Berwald space is one of the generalizations of Berwald spaces. In the present paper, we considered a cubic (a, ß)-metric which is a special class of p-power Finsler metric and obtained the conditions under which the Finsler space with such special metric will be a Weakly-Berwald space. [ABSTRACT FROM AUTHOR]

Igarashi introduce the concept of (α, β)-metric in Cartan space ln analogously to one in Finsler space and obtained the basic important geometric properties and also investigate the special class of the space with (α, β)-metric in ln in terms of 'invariants' . In the present paper, we determine the 'invariants' in two different cases of deformed infinite series metric, which characterize the special classes of Cartan spaces ln .Further, we investigate some classes of deformed infinite series spaces and obtain deformed infinite series class which will provide the example of Cartan spaces. [ABSTRACT FROM AUTHOR]

The purpose of present paper to determine the Finsler spaces due to deformation of special Finsler (α, β)-metric. Consequently, we obtained the non-holonomic frame with the help of α² = aij(x)yiyj, one form metric β = bi(x)yi and infinite series of (α, β) metric such as the forms I: (***) + α² = F¹2 + F²2 i.e. sum of the square of infinite series of (_, β)-metric and square of Riemannian metric II: (***) + α² = F²1 + F²3 i.e. sum of the square of infinite series of (_, β)-metric and square of 1-form metric. [ABSTRACT FROM AUTHOR]

The purpose of present paper to determine the Finsler spaces due to deformation of special Finsler (α, β)-metric. Consequently, we obtained the non-holonomic frame with the help of Riemannian metric α 2 = aij (x)yiyj, one form metric β = bi(x)y i and infinite series of (α, β) metric such as the forms I. ( β²/β−α )α = αβ²/β−α i.e. product of the infinite series of (α, β)-metric and Riemannian metric II. ( β²/β−α )β = β³/β−α i.e. product of the infinite series of (α, β)-metric and 1-form metric. [ABSTRACT FROM AUTHOR]

In the present paper we have studied the Finslerian hypersurfaces of a Finsler space with the special form of exponential (α, β)- metric such as L (α, β) = αeβ/α + βe-β/α. We also examined the hypersurfaces of this special exponential metric as a hyperplane of first, second and third kinds. [ABSTRACT FROM AUTHOR]

The rationale of this paper is to study the Finslerian hypersurfaces of a Finsler space with the special deformed Berwald-Infinite series metric. Further examined under which condition, the Finslerian hypersurfaces of this special metric becomes a hyperplane of first, second and third kinds. [ABSTRACT FROM AUTHOR]

The purpose of this work is to explore a special class of p-power Finsler metric called the cubic (α,β)-metric and to determine the circumstances under which the Finsler space containing such a special metric will be locally Minkowskian and Conformally at. Furthermore, we proved that under homothetic Conformal transformation, this metric is Conformally Minkowskian and Conformally Berwald. [ABSTRACT FROM AUTHOR]

The equation of geodesic in a two-dimensional Finsler space is given by Matsumoto and Park for Finsler space with a (α,β)- metric in the year 1997 and 1998. Further Park and Lee studied the above case for generalized Kropina metric in the year 2000. Recently Chaubey and his co-authors studied the same for some special (α,β)- metric in 2013 and 2014. In continuation of this the purpose of present paper is to express the differential equations of geodesics in a two-dimensional Finsler space with some special Finsler (α,β)- metric. [ABSTRACT FROM AUTHOR]

The purpose of present paper is to study the T-tensor of such a Finsler space with the condition L2(α, β)C = β, where α = √ aij(x)yiyj and β = biyi and get some important theorems. We shall also obtain the condition for such a Finsler space to be a Landsberg space or Berwald space. The notations and terminologies are referred to the monograph [7].In this paper we introduce and study a new subclass of meromorphically uniformly convex functions with positive coefficients defined by a differential operator and obtain coefficient estimates, growth and distortion theorem, radius of convexity, integral transforms, convex linear combinations, convolution properties and δ-neighborhoods for the class σp(α). [ABSTRACT FROM AUTHOR]

The purpose of present paper to determine the Finsler spaces due to deformation of special Finsler (α, β) metrics. Consequently, we obtain the nonholonomic frame with the help of Riemannian metric α2 = aij(x)yiyj, one form metric β = bi(x)yi and Douglas metric ... such as forms .... The first metric of the above deformation is obtained by the product of Riemannian metric and one form and second one is the product of Douglas metric and 1-form metric. [ABSTRACT FROM AUTHOR]

In the present paper we have studied the Finslerian hypersurfaces of a Finsler space with the special deformed Berwald-Matsumoto metric. We also examined the hypersurfaces of this special metric as a hyperplane of first, second and third kinds. [ABSTRACT FROM AUTHOR]

In the year 1998, M. Matsumoto [11] has studied the conditions for some Finsler spaces with (α, β)-metric to be of Douglas type. The purpose of the present paper is devoted to find the various conditions for a Finsler space Fn with a special (α, β)-metric to be a Douglas space for assumptions α² = 0(modβ), in the entire paper. [ABSTRACT FROM AUTHOR]

The purpose of present paper is to find the nonholonomic frames for the deformed Matsumoto type metric which are given in the forms I: (α2/α-β )α = α3 α-β II: (α2/α-β)β = α2β α-β where α2 = aij(x)yiyj and β = bi(x)yi. The first metric of the above deformation is obtained by the product of Matsumoto and Riemannian metric and second one is the product of Matsumoto and 1-form metric. [ABSTRACT FROM AUTHOR]

The concept of locally dually flat Finsler metrics originate from information geometry. As we know, (α, β) - metrics defined by a Riemannian metric α and a 1-form β, represent an important class of Finsler metrics .In the year 2014, S. K. Narasimhamurthy,A.R. Kavyashree and Y. K. Mallikarjun obtained characterization of locally first approximate Matsumoto metric [1].In continuation of the paper we study and characterize locally dually flat for a special Finsler (α, β) metric F = α+β+β2/α+β3/α2with isotropic S-curvature, which is not Riemannian. [ABSTRACT FROM AUTHOR]

The purpose of present paper to determine the two special Finsler spaces due to deformations of some special Finsler space with help of (α,β)-metrics. Consequently, we obtain the non-holonomic frame for the (α,β)-metrics, such as (I) L = (α²/α-β) β²/α = αβ/(α-β) i.e. product of Matsumoto metric and Kropina metric and (II) L = (α + β) β²/α = β² + β³/α i.e. product of Randers metric and Kropina metric. [ABSTRACT FROM AUTHOR]