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30 sonuçtan 1-3 arası sonuçlar
Sayfa 472
Hence, this expression is close to an affine combination of the second derivatives
of the metric tensor. Thus, for the set of numbers it1, v' we can consider the
following quantities: 1) the formal curvature Ki; 2) the quantity K2 obtained by ...
Hence, this expression is close to an affine combination of the second derivatives
of the metric tensor. Thus, for the set of numbers it1, v' we can consider the
following quantities: 1) the formal curvature Ki; 2) the quantity K2 obtained by ...
Sayfa 468
0 ) Let ( , ) and ( : , : ) 1 denote the Riemannian metrics ( i . e . , the corresponding
scalar products ) on Mo and M1 , respectively . There exists a natural smooth
structure on M relative to which Mo and My are smooth submanifolds . However ,
in ...
0 ) Let ( , ) and ( : , : ) 1 denote the Riemannian metrics ( i . e . , the corresponding
scalar products ) on Mo and M1 , respectively . There exists a natural smooth
structure on M relative to which Mo and My are smooth submanifolds . However ,
in ...
Sayfa 471
The coefficients of the metric tensor ( ; - ) ( 8 ) belong to the Sobolev class W2 . .
Proof . Observe that the metric tensor ( : , : ) ( 6 ) may fail to be C2 - smooth
because the second derivatives admit jumps on T . However , the first derivatives
are ...
The coefficients of the metric tensor ( ; - ) ( 8 ) belong to the Sobolev class W2 . .
Proof . Observe that the metric tensor ( : , : ) ( 6 ) may fail to be C2 - smooth
because the second derivatives admit jumps on T . However , the first derivatives
are ...
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algebraic analytic apply assume basis boundary bounded called chain homotopy closed coefficients complex computation condition connection Consequently consider constant construction contains continuous convex corresponding defined definition deformation denote determined differential domain element equal equation equivalence estimate example exists extension fact field finite fixed formula function given identity implies inequality integral intersection introduce invariant inverse isomorphism Lemma linear Math Mathematical matrix measure metric Moreover natural normal Observe obtain Obviously operator orientation particular periodic positive present problem projective Proof properties Proposition prove regular relation Remark respectively result ring satisfies scheme sequence singular smooth solutions space standard statement Subsection suffices Suppose takes Theorem theory transformation true twists unique vector weight zero