Geometry of second-order connections and ordinary differential equations
نویسندگان
چکیده
منابع مشابه
Recurrent metrics in the geometry of second order differential equations
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 ...
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The main purposes of this article are to extend our previous results on homogeneous sprays [15] to arbitrary secondorder differential equations, to show that locally diffeomorphic exponential maps can be defined for any of them, and to give a (possibly nonlinear) covariant derivative for any (possibly nonlinear) connection. In the process, we introduce vertically homogeneous connections. Unlike...
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متن کاملrecurrent metrics in the geometry of second order differential equations
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 ...
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ژورنال
عنوان ژورنال: Mathematica Bohemica
سال: 1995
ISSN: 0862-7959,2464-7136
DOI: 10.21136/mb.1995.126226