Differentiable Riemannian geometry

BHEEMA NAYAK. K, MESA KALPANA, DASI SANDHYA

Abstract


Abstract   In  this   paper   uniform   upper and  lower            Definition 2.1.5

 

i

i

j

i

j

j

i

j

continuous function  f  Î (M ) on manifolds spaces with    If (U Ç U )¹ then the diffeomorphism

curvature bounds on (M ) as surfaces and applications


(U Ç U


)® (U Ç U


) is known as the


compact Riemannian boundary (f , f -1 )ÎM ± Î R


is     ( transitition map ).


complete with Riemannian and we prove is integration on differential on R

 



Keywords


Basic differential geometry – differentiable manifolds charts – integration smooth manifolds.



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