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Showing posts from December 17, 2018

Síria nos Jogos Olímpicos de Verão de 2016

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Síria nos Jogos Olímpicos de Verão de 2016 Comitê Olímpico Nacional Código do COI SYR Nome Syrian Olympic Committee site oficial (em inglês) Jogos Olímpicos de Verão de 2016 Sede Rio de Janeiro, Brasil Competidores 7 em 5 esportes Porta-bandeira Majd Eddin Ghazal Medalhas Pos. n/d 0 0 0 0 Participações nos Jogos Olímpicos Verão 1948 • 1952 • 1956 • 1960 • 1964 • 1968 • 1972 • 1976 • 1980 • 1984 • 1988 • 1992 • 1996 • 2000 • 2004 • 2008 • 2012 • 2016 Outras participações relacionadas UAR República Árabe Unida (1960–1964)

Well-definedness of assinging a value to a point of a manifold with respect to parallelism

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up vote 1 down vote favorite By definition as in DoCarmo’s Riemannian Geometry book, in a smooth manifold $M$ a vector field $V$ along a smooth curve $c:(a,b)rightarrow M$ is a mapping $tmapsto V(t)in T_{c(t)}M$ such that $tmapsto V(t)f$ is a smooth map for all smooth maps $fin C^{infty}(M)$ . Suppose that $c_1,c_2$ are two smooth curves in $M$ such that $c_1(t_0)=c_2(t_0)$ , and $c_1(t_1)=c_2(t_1)$ where $t_0$ and $t_1$ are two distinct points in the (same) domain of $c_1,c_2$ . Suppose that $V_0in T_{c_1(t_0)}M$ . There exists a unique parallel vector field $V_1$ along $c_1$ such that $V_1(t_0)=V_0$ , and similarly a unique $V_2$ along $c_2$ such that $V_2(t_0)=V_0$ . Does it follow that $V_1(t_1)=V_2(t_1)$ ? differential-geometry riemannian-geometry smooth-manifolds