. "Diferenci\u00E1ln\u00ED invarianty z vno\u0159en\u00ED variet s metrick\u00FDmi poli"@cs . . "2"^^ . "RIV/00216224:14310/04:00010215" . "Differential Invariants of Immersions of Manifolds with Metric Fields"@en . . . . . . "Differential Invariants of Immersions of Manifolds with Metric Fields" . "2" . . . "DE - Spolkov\u00E1 republika N\u011Bmecko" . "11"^^ . "The problem of finding all r-th order differential invariants of immersions of manifolds with metric fields, with values in a left (G^1_m x G^1_n)-manifold is formulated. For obtaining the basis of higher order differential invariants the orbit reduction method is used. As a new result it appears that r-th order differential invariants depending on an immersion f:M->N of manifolds M and N and on metric fields on them can be factorized through metrics, curvature tensors and their covariant derivatives up to the order (r-2), and covariant differentials of the tangent mapping Tf up to the order r. The concept of a covariant differential Tf is also introduced in this paper. The obtained results are geometrically interpreted as well." . . "Communications in Mathematical Physics" . "Differential Invariants of Immersions of Manifolds with Metric Fields"@en . "560574" . . "0010-3616" . . . . . "Musilov\u00E1, Jana" . "The problem of finding all r-th order differential invariants of immersions of manifolds with metric fields, with values in a left (G^1_m x G^1_n)-manifold is formulated. For obtaining the basis of higher order differential invariants the orbit reduction method is used. As a new result it appears that r-th order differential invariants depending on an immersion f:M->N of manifolds M and N and on metric fields on them can be factorized through metrics, curvature tensors and their covariant derivatives up to the order (r-2), and covariant differentials of the tangent mapping Tf up to the order r. The concept of a covariant differential Tf is also introduced in this paper. The obtained results are geometrically interpreted as well."@en . "smooth manifolds; differential invariants"@en . "Diferenci\u00E1ln\u00ED invarianty z vno\u0159en\u00ED variet s metrick\u00FDmi poli"@cs . "RIV/00216224:14310/04:00010215!RIV09-GA0-14310___" . "P(GA201/03/0512), Z(MSM 143100006)" . "14310" . "249" . "Je formulov\u00E1n probl\u00E9m nalezen\u00ED v\u0161ech diferenci\u00E1ln\u00EDch invariant\u016F r-t\u00E9ho \u0159\u00E1du z vno\u0159en\u00ED variet s metrick\u00FDmi poli, s hodnotami v lev\u00E9 (G^1_m x G^1_n)-variet\u011B. B\u00E1ze invariant\u016F je z\u00EDsk\u00E1na pomoc\u00E9 metody redukce orbit. Jako nov\u00FD v\u00FDsledek je dok\u00E1z\u00E1no, \u017Ee diferenci\u00E1ln\u00ED invarianty r-t\u00E9ho \u0159\u00E1du z vno\u0159en\u00ED f:M->N variet M a N s metrick\u00FDmi poli lze faktorizovet vzhledem k metrik\u00E1m, k\u0159ivostem a jejich kovarintn\u00EDm rerivac\u00EDm do \u0159\u00E1du (r-2) a kovariantn\u00EDmu diferenci\u00E1lu te\u010Dn\u00E9ho zobrazen\u00ED Tf do \u0159\u00E1du r. posledn\u00ED pojem je v pr\u00E1ci nov\u011B zaveden. Z\u00EDskan\u00E9 v\u00FDsledky jsou interpretov\u00E1ny geometricky."@cs . "000222914800005" . . "Musilov\u00E1, Pavla" . "[6DC65568A0EA]" . "2"^^ . "Differential Invariants of Immersions of Manifolds with Metric Fields" . .