It is well known that no non-trivial Killing vector field exists on a compact Riemannian manifold of negative Ricci curvature; analogously, no non-trivial harmonic one-form exists on a compact manifold of positive Ricci curvature. One can consider the following, more general, problem. By reducing the assumption on the Ricci curvature to one on the scalar curvature, such vanishing theorems canno...

We prove that a Ricci curvature based method of triangulation of compact Riemannian manifolds, due to Grove and Petersen, extends to the context of weighted Riemannian manifolds and more general metric measure spaces. In both cases the role of the lower bound on Ricci curvature is replaced by the curvature-dimension condition CD(K,N). We show also that for weighted Riemannian manifolds the tria...

dually flat finsler metrics form a special and valuable class of finsler metrics in finsler information geometry,which play a very important role in studying flat finsler information structure. in this paper, we prove that everylocally dually flat generalized randers metric with isotropic s-curvature is locally minkowskian.

(i) A subgroup of PFL(d, q) containing PSL(d, q), in its usual 2-transitive representation; (ii) A collineation group of AG(d, q), containing the group ASL(d, q) of collineations generated by elations, in its usual 2-transitive representation on AG(d, q); (iii) A 7 in its 2-transitive representation of degree 15; (iv) There is a regular normal subgroup, and if x~S then F x acts on S { x } as th...

In this paper we describe a method to compute the collineation matrix between two unmatched images of an unknown planar contour described using a B-spline snake. The two images of the contour are matched and the collineationmatrix is used to servo a camera mounted on the robot end-e ector using a 2 1/2 D visual servoing technique. The experimental results, obtained using common planar objects, ...