Intersection theorems for Finsler manifolds (Q2714281)

\textit{T. Frankel} [Pac. J. Math. 11, 165--171 (1961; Zbl 0107.39002)] proved that two compact, totally geodesic submanifolds \(V\) and \(W\) of a complete connected Riemannian manifold \(M\) with positive sectional curvature always have a nonempty intersection provided \(\dim V+\dim W\geq \dim M\). Analogous result is true if \(M\) is a complete connected Kählerian manifold of positive sectional curvature, and \(V\) and \(W\) are compact complex submanifolds. These results have been extended e.g. to the case of nearly/quaternionic/locally conformal Kähler manifolds. In the paper the authors generalize Frankel's theorems for Finsler and Kähler Finsler manifolds. The assumptions in the second Frankel's theorem are slightly different from the original: \(V\) and \(W\) are two compact complex analytic submanifolds of a Kähler Finsler manifold \(M\) of positive holomorphic bisectional curvature and vanishing \((1,1)\)-torsion.