Some connectedness problems in positively curved Finsler manifolds

This paper studies some connectedness problems under the positivity hypothesis of various curvatures (k$k$-Ricci and flag curvature). Our approach uses Morse Theory for general end conditions (see Ioan Radu Peter, The Morse index theorem where the ends are submanifolds in Finsler geometry, Houston J. Math. 32 (4) (2006) 995–1009]). Some previous results related to the flag curvature were obtained in Ioan Radu Peter, A connectedness principle in positively curved Finsler manifolds, in: H. Shimada, S. Sabau (Eds.), Advanced Studies in Pure Mathematics, Finsler Geometry, Sapporo 2005-In Memory of Makoto Matsumoto, Mathematical Society of Japan, 2007]. Some results from Riemannian geometry are extended to the Finsler category also. The Finsler setting is much more complicated and the difference between Finsler and Riemann settings will be emphasized during the paper.