Asisknown, theLagrangeandHamiltongeometrieshaveappearedrelatively recently 76, 86]. Since 1980thesegeometrieshave beenintensivelystudied bymathematiciansandphysicistsfromRomania, Canada, Germany, Japan, Russia, Hungary, e.S.A. etc. PrestigiousscientificmeetingsdevotedtoLagrangeandHamiltongeome tries and their applications have been organized in the above mentioned countries and a number ofbooks and monographs have been published by specialists in the field: R. Miron 94, 95], R. Mironand M. Anastasiei 99, 100], R. Miron, D. Hrimiuc, H. Shimadaand S.Sabau 115], P.L. Antonelli, R....