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@article{556845,
author = {Musilová, Pavla and Musilová, Jana},
article_location = {Heidelberg},
article_number = {2},
keywords = {smooth manifolds; differential invariants},
language = {eng},
issn = {0010-3616},
journal = {Communications in Mathematical Physics},
title = {Differential Invariants of Immersions of Manifolds with Metric Fields},
volume = {249},
year = {2004}
}
TY - JOUR
ID - 556845
AU - Musilová, Pavla - Musilová, Jana
PY - 2004
TI - Differential Invariants of Immersions of Manifolds with Metric Fields
JF - Communications in Mathematical Physics
VL - 249
IS - 2
SP - 319-329
EP - 319-329
PB - Springer-Verlag
SN - 00103616
KW - smooth manifolds
KW - differential invariants
N2 - 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.
ER -
MUSILOVÁ, Pavla and Jana MUSILOVÁ. Differential Invariants of Immersions of Manifolds with Metric Fields. \textit{Communications in Mathematical Physics}. Heidelberg: Springer-Verlag, 2004, vol.~249, No~2, p.~319-329. ISSN~0010-3616.
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