A Nakano type inequality for mixed forms on complex Finsler manifolds

Relative volume comparison theorems in Finsler geometry and their applications

We establish some relative volume comparison theorems for extremal volume forms of‎ ‎Finsler manifolds under suitable curvature bounds‎. ‎As their applications‎, ‎we obtain some results on curvature and topology of Finsler manifolds‎. ‎Our results remove the usual assumption on S-curvature that is needed in the literature‎.

On the k-nullity foliations in Finsler geometry

Here, a Finsler manifold $(M,F)$ is considered with corresponding curvature tensor, regarded as $2$-forms on the bundle of non-zero tangent vectors. Certain subspaces of the tangent spaces of $M$ determined by the curvature are introduced and called $k$-nullity foliations of the curvature operator. It is shown that if the dimension of foliation is constant, then the distribution is involutive...

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...

Stable Exponentially Harmonic Maps Between Finsler Manifolds

ACTA UNIVERSITATIS APULENSIS No 18/2009 ON VECTOR-BUNDLE VALUED COHOMOLOGY ON COMPLEX FINSLER MANIFOLDS

In this paper we define a complex adapted connection of type Bott on vertical bundle of a complex Finsler manifold. When this connection is flat we get a vertical vector valued cohomology. The notions are introduced by analogy with the real case for foliations. Finally, using the partial Bott connection we give a characterization of strongly Kähler-Finsler manifolds. 2000 Mathematics Subject Cl...