Geometry of Legendrian knots.

We study the extrinsic geometry of Legendrian knots in the standard tight contact structure on In particular, we show that the total curvature of a Legendrian knot in is bounded below by times, the total number of cusps in the front projection of . We also show that a Legendrian -torus knot has the total curvature bounded below by while that of the Legendrian knots is bounded below by . Furthermore, we find an explicit relation between the Thurston-Bennequin number of a Legendrian knot and the geometric self-linking number, the curvature and the torsion of the knot . [ABSTRACT FROM AUTHOR]