LICHNEROWICZ CONNECTIONS IN ALMOST COMPLEX FINSLER MANIFOLDS

Special connections in almost paracontact metric geometry

‎Two types of properties for linear connections (natural and almost paracontact metric) are discussed in almost paracontact metric geometry with respect to four linear connections‎: ‎Levi-Civita‎, ‎canonical (Zamkovoy)‎, ‎Golab and generalized dual‎. ‎Their relationship is also analyzed with a special view towards their curvature‎. ‎The particular case of an almost paracosymplectic manifold giv...

The Lichnerowicz theorem on CR manifolds

For any compact strictly pseudoconvex CR manifold M endowed with a contact form θ we obtain the Bochner type formula 1 2 ∆b(|∇f |2) = |πH∇f |2 + (∇f)(∆bf) + ρ(∇Hf,∇Hf) + 2Lf (involving the sublaplacian ∆b and the pseudohermitian Ricci curvature ρ). WhenM is compact of CR dimension n and ρ(X,X)+ 2A(X, JX) ≥ k Gθ(X,X), X ∈ H(M), we derive the estimate −λ ≥ 2nk/(2n− 1) on each nonzero eigenvalue λ...

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...

Wong-rosay Theorem in Almost Complex Manifolds

We study the compactness of sequences of diffeomorphisms in almost complex manifolds in terms of the direct images of the standard integrable structure.

Stable Exponentially Harmonic Maps Between Finsler Manifolds