$G_2$-geometry in contact geometry of second order
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 ...
متن کاملGeometry of Linear Differential Systems –towards– Contact Geometry of Second Order
where Jx = Gr(Tx(M), n) is the Grassmann manifold of all n-dimensional subspaces of the tangent space Tx(M) to M at x. Each element u ∈ J(M,n) is a linear subspace of Tx(M) of codimension m, where x = π(u). Hence we have a differential system C of codimension m on J(M,n) by putting: C(u) = π−1 ∗ (u) ⊂ Tu(J(M,n)) π∗ −→ Tx(M). for each u ∈ J(M,n). C is called the Canonical System on J(M,n). We ca...
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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2 Contact manifolds 4 2.1 Contact manifolds and their submanifolds . . . . . . . . . . . . . . 6 2.2 Gray stability and the Moser trick . . . . . . . . . . . . . . . . . . 13 2.3 Contact Hamiltonians . . . . . . . . . . . . . . . . . . . . . . . . . 16 2.4 Darboux’s theorem and neighbourhood theorems . . . . . . . . . . 17 2.4.1 Darboux’s theorem . . . . . . . . . . . . . . . . . . . . . . . 17...
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ژورنال
عنوان ژورنال: Methods and Applications of Analysis
سال: 2019
ISSN: 1073-2772,1945-0001
DOI: 10.4310/maa.2019.v26.n1.a4