Conformal transformation of Douglas space of second kind with special (α, β)-metric

PurposeIn this paper, the authors prove that the Douglas space of second kind with a generalised form of special (α, β)-metric F, is conformally invariant.Design/methodology/approachFor, the authors have used the notion of conformal transformation and Douglas space.FindingsThe authors found some results to show that the Douglas space of second kind with certain (α, β)-metrics such as Randers metric, first approximate Matsumoto metric along with some special (α, β)-metrics, is invariant under a conformal change.Originality/valueThe authors introduced Douglas space of second kind and established conditions under which it can be transformed to a Douglas space of second kind.

On a Hypersurface of a Finsler Space with Randers Change of Matsumoto Metric

The present paper contains certain geometrical properties of a hypersurface of a Finsler space with Randers change of Matsumoto metric.

HORIZONTAL LAPLACIAN ON TANGENT BUNDLE OF FINSLER MANIFOLD WITH g-NATURAL METRIC

Recently the third author studied horizontal Laplacians in real Finsler vector bundles and complex Finsler manifolds. In this paper, we introduce a class of g-natural metrics Ga,b on the tangent bundle of a Finsler manifold (M, F) which generalizes the associated Sasaki–Matsumoto metric and Miron metric. We obtain the Weitzenböck formula of the horizontal Laplacian associated to Ga,b, which is a second-order differential operator for general forms on tangent bundle. Using the horizontal Laplacian associated to Ga,b, we give some characterizations of certain objects which are geometric interest (e.g. scalar and vector fields which are horizontal covariant constant) on the tangent bundle. Furthermore, Killing vector fields associated to Ga,b are investigated.