Differential geometry in the large

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 ...

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 ...

Geometry II - Discrete Differential Geometry

Topics in Differential Geometry

In less than two pages (pp. 54–55) the Campbell-Baker-Hausdorff formula is taken care of, in a proof containing exactly forty-eight English words: the rest is algebraic manipulation. For some of us, myself included, this is an exposition devoutly-to-be-wished; for the complementary set of readers it’s something a lot less than palatable. So, given that Peter W. Michor’s Topics in Differential G...

Differential Geometry in Toposes

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