?? talking with curtis pro about jacobi fields and riemannian submersions and so forth ...

?? space / stack of geodesics of a riemannian manifold .... ???? .... interpretation of jacobi field in thois context .... ?? case of torus ??? .....

?? special case of 3-sphere ... relationship to pgl(4) incidence geometry .... ???? .....

?? getting "positive contact flow" from riemannian metric ... ?? how close this process is to being reversible ... ??? ....

?? trying to relate minimalish example of riemannian submersion with non-integrable horizontal distribution to nice simple contact distribution .... ??? .... ??? ....

?? situation where wavefront advances to geodesic .... ???? ...... ?? hmm, only in 2d case ... and special even there ?? ... ???? ...

?? gradient of scalar curvature .... ?? ....

?? closed geodesics .... ??? ....

?? for which surfaces are all geodesics closed ??? .... ??? ....

??? vague memory about "bott periodicity" and geodesics and "jacobi ..." .... ???? .....

?? jacobi field as special case of .... ??? ... "deformation of trajectory of dunamical system" .... ???? ....