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The notion of holomorphic bisectional curvature for a complex Finsler space (M, F ) is defined with respect to the Chern complex linear connection on the pull-back tangent bundle. By means of holomorphic curvature and holomorphic flag curvature of a complex Finsler space, a special approach is emloyed to obtain the characterizations of the holomorphic bisectional curvature. For the class of gen...

Adopting the pullback formalism, a new linear connection in Finsler geometry has been introduced and investigated.
 Such unifies all formerly known connections some other not so far. Also, our is Finslerian version of Tripathi Riemannian geometry. The existence uniqueness such are proved intrinsically. An explicit intrinsic expression relating this to Cartan obtained. Some generalized cons...

In [Mu1] we underlined the motifs of holomorphic subspaces in a complex Finsler space: induced nonlinear connection, coupling connections, and the induced tangent and normal connections. In the present paper we investigate the equations of Gauss, H−and A−Codazzi, and Ricci equations of a holomorphic subspace. We deduce the link between the holomorphic curvatures of the Chern-Finsler connection ...

We survey the geometry of Lagrange and Finsler spaces and discuss the issues related to the definition of curvature of nonholonomic manifolds enabled with nonlinear connection structure. It is proved that any commutative Riemannian geometry (in general, any Riemann– Cartan space) defined by a generic off–diagonal metric structure (with an additional affine connection possessing nontrivial torsi...

Adopting the pullback approach to Finsler geometry, the aim of the present paper is to provide new intrinsic (coordinate-free) proofs of intrinsic versions of the existence and uniqueness theorems for the Cartan and Berwald connections on a Finsler manifold. To accomplish this, the notions of semispray and nonlinear connection associated with a given regular connection, in the pullback bundle, ...

In this paper, it is elaborated the theory the Ricci flows for manifolds enabled with nonintegrable (nonholonomic) distributions defining nonlinear connection structures. Such manifolds provide a unified geometric arena for nonholonomic Riemannian spaces, Lagrange mechanics, Finsler geometry, and various models of gravity (the Einstein theory and string, or gauge, generalizations). We follow th...

We elaborate an unified geometric approach to classical mechanics, Riemann–Finsler spaces and gravity theories on Lie algebroids provided with nonlinear connection (N–connection) structure. There are investigated the conditions when the fundamental geometric objects like the anchor, metric and linear connection, almost sympletic and related almost complex structures may be canonically defined b...

Munteanu (Complex spaces in Finsler, Lagrange and Hamilton Geometries, Kluwer Academic Publishers, Dordrecht, 2004) defined the canonical connection associated to a strongly pseudoconvex complex Finsler manifold (M, F). We first prove that holomorphic sectional curvature tensors of coincide with those Chern–Finsler F if only is Kähler-Finsler metric. also investigate relationship Ricci curvatur...

The present paper deals with an intrinsic investigation of the notion of a concurrent π-vector field on the pullback bundle of a Finsler manifold (M,L). The effect of the existence of a concurrent π-vector field on some important special Finsler spaces is studied. An intrinsic investigation of a particular β-change, namely the energy β-change (L̃(x, y) = L(x, y) + B(x, y)with B := g(ζ, η); ζ bei...