If you're on a sphere, rotating the geodesic would give you a conjugate point at distance $\pi$, while moving the geodesic would give you a conjugate point at distance $\frac$. Let M be a complete Riemannian manifold with some conditions on. I haven't found a good picture or description of the other direction, but I suspect you can essentially "move the geodesic in space" in that direction. There are many theorems in the differential geometry literature of the following sort. In all the normal directions, the the simple thing you can do is "rotate the geodesic in that direction" (see Lemmas 10.7 and 10.8, as well as the figure). you get a reparametrisation of the same geodesic. It seems like tangential components are "trivial", i.e. Riemannian Manifold, Riemannian Geometry, Riemannian Geometry Sakai Takashi American, Space Time Curvature Quantum Field Theory, Riemannian. Try it out now PDF riemannian geometry (Full Book Download) - riemannian geometry wilhelm klingenberg 939, riemannian geometry ebook chumipyzafid. These correspond to independent, arbitrary choices of $J(0) \in T_p (M)$ and $D_t J(0) \in T_p M$. Download Film Naruto Vs Pain Sub Indo on this page. Lee states that the set of Jacobi fields along a geodesic is a $2n$-dimensional linear space (Corollary 10.5), with 2 tangential dimensions and $2n-2$ normal dimensions. Lee's Riemannian Manifolds: An Introduction to Curvature ( ), Figure 10.4.
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