– in this paper we consider some (α ,β ) -metrics such as generalized kropina, matsumoto and f (α β )2α = + metrics, and obtain necessary and sufficient conditions for them to be einstein metrics when βis a constant killing form. then we prove with this assumption that the mentioned einstein metrics must beriemannian or ricci flat.

We establish quaternionic contact (qc) versions of the so called Almost Schur Lemma, which give estimations qc scalar curvature on a compact manifold to be constant in terms norm $$[-1]$$ -component and trace-free part [3]-component horizontal Ricci tensor torsion endomorphism, under certain positivity conditions.

the main objective of this paper is to find the necessary and sufficient condition of a given finslermetric to be einstein in order to classify the einstein finsler metrics on a compact manifold. the consideredeinstein finsler metric in the study describes all different kinds of einstein metrics which are pointwiseprojective to the given one. this study has resulted in the following theorem tha...

In [4], Gurevich, Pyatov and Saponov stated an expansion for the product of two Schur functions and gave a proof based on the Plücker relations. Here we show that this identity is in fact a special case of a quite general Schur function identity, which was stated and proved in [1, Lemma 16]. In [1], it was used to prove bijectively Dodgson’s condensation formula and the Plücker relations, but w...

and Applied Analysis 3 denotes a class of continuous functions f(x, t) : R × [0, +∞) → R n satisfying (x − y) T P (f (x, t) − f (y, t) − Δ (x − y)) ≤ −η(x − y) T (x − y) (4) for some η > 0, all x, y ∈ R and all t ≥ 0. Lemma 4 (Schur complement [25]). The following linear matrix inequality (LMI)