recurrent metrics in the geometry of second order differential equations

Authors

mircea crasmareanu

faculty of mathematics university "al. i. cuza" iasi, 700506

abstract

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 nonlinear connection of the semispray $s$. also, the weyl connection of conformal gauge theories is obtained as a particular case.

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Journal title:
bulletin of the iranian mathematical society

جلد ۳۸، شماره ۲، صفحات ۳۹۱-۴۰۱

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