A Lichnerowicz–Obata–Cheng Type Theorem on Finsler Manifolds

Galloway’s compactness theorem on Finsler manifolds

The compactness theorem of Galloway is a stronger version of the Bonnet-Myers theorem allowing the Ricci scalar to take also negative values from a set of real numbers which is bounded below. In this paper we allow any negative value for the Ricci scalar, and adding a condition on its average, we find again that the manifold is compact and provide an upper bound of its diameter. Also, with no c...

On Stretch curvature of Finsler manifolds

In this paper, Finsler metrics with relatively non-negative (resp. non-positive), isotropic and constant stretch curvature are studied.  In particular, it is showed that every compact Finsler manifold with relatively non-positive (resp. non-negative) stretch curvature is a Landsberg metric. Also, it is proved that every  (α,β)-metric of non-zero constant flag curvature and non-zero relatively i...

On concircularly recurrent Finsler manifolds

Two special Finsler spaces have been introduced and investigated, namely R-recurrent Finsler space and concircularly recurrent Finsler space. The defining properties of these spaces are formulated in terms of the first curvature tensor of Cartan connection. The following three results constitute the main object of the present paper: (i) a concircularly flat Finsler manifold is necessarily of co...

Stable Exponentially Harmonic Maps Between Finsler Manifolds

A Hodge decomposition theorem on strongly pseudoconvex compact complex Finsler manifolds

In this paper, we prove that the Hodge-Laplace operator on strongly pseudoconvex compact complex Finsler manifolds is a self-adjoint elliptic operator. Then, from the decomposition theorem for self-adjoint elliptic operators, we obtain a Hodge decomposition theorem on strongly pseudoconvex compact complex Finsler manifolds. M.S.C. 2010: 53C56, 32Q99.