Tiwari, Amitabh2012-05-022012-05-02198963p.http://hdl.handle.net/10263/3707This thesis is under the supervision of Dr.Amiya MukherjeeenCurvatureLeft invariant metricsParametric homotopyCurvatures of left invariant metrics on lie group and parametric homotopy principles for a class of partial differential relations on closed manifoldsThesis