On New Classes of Stretch Minkowskian Product Finsler Manifolds

Let (M1,F1) and (M2,F2) be two Finsler manifolds. A Minkowskian product Finsler manifold is defined to be the product manifold M1×M2, which is endowed with a Finsler metric F. This metric F is constructed by taking the square root of a product function f, which itself operates on the squares of the original metrics F1 and F2. This paper focuses on new classes of stretch Minkowskian product Finsler manifolds. We prove that the Minkowskian product Finsler manifold (M,F) is a B˜-manifold (resp. B˜-stretch manifold, H-stretch manifold) if and only if (M1,F1) and (M2,F2) are both B˜-manifold (resp. B˜-stretch manifold, H-stretch manifold). Thus an effective method for constructing special Finsler manifolds mentioned above is given.