given a pair (semispray $s$, metric $g$) on a tangent bundle, the family of nonlinear connections $n$ such that $g$ is recurrent with respect to $(s, n)$ with a fixed recurrent factor is determined by using the obata tensors. in particular, we obtain a characterization for a pair $(n, g)$ to be recurrent as well as for the triple $(s, stackrel{c}{n}, g)$ where $stackrel{c}{n}$ is the canonical ...

Toshio Obata1, Michiko Nakashima2 1Faculty of Health Sciences, Osaka Aoyama University, School of Nursing Niina, Mino City, Japan. 2Department of Nursing, School of Health Siences, Asahi University, 1851 Hozumi Mizuho City Gifu, Japan. Corresponding Author: Toshio Obata, Osaka Aoyama University, Faculty of Health Sciences, School of Nursing Niina, Mino City, Japan.Ankara, Turkey. Tel: +81-72-73...

Given a pair (semispray $S$, metric $g$) on a tangent bundle, the family of nonlinear connections $N$ such that $g$ is recurrent with respect to $(S, N)$ with a fixed recurrent factor is determined by using the Obata tensors. In particular, we obtain a characterization for a pair $(N, g)$ to be recurrent as well as for the triple $(S, stackrel{c}{N}, g)$ where $stackrel{c}{N}$ is the canonical ...

We solve two classical conjectures by showing that if an action of a connected Lie group on a complete Riemannian manifold preserves the geodesics (considered as unparameterized curves), then the metric has constant positive sectional curvature, or the group acts by affine transformations.