Результаты исследований: Научные публикации в периодических изданиях › статья › Рецензирование
The algebra of generalized Jacobi fields. / Kal'nitskii, V. S.
в: Journal of Mathematical Sciences, Том 91, № 6, 1998, стр. 3476-3491.Результаты исследований: Научные публикации в периодических изданиях › статья › Рецензирование
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TY - JOUR
T1 - The algebra of generalized Jacobi fields
AU - Kal'nitskii, V. S.
PY - 1998
Y1 - 1998
N2 - We study the structure of those vector fields on the tangent bundle of an arbitrary smooth manifold which commute with the geodesic vector field defined by an affine connection. The study is restricted to polylinear fields generated by a pair of symmetric pseudotensor fields of type (k, 1) and (k + 1, 1), k ≥ 0, defined on the manifold. We establish an isomorphism between the space of infinitesimal automorphisms of fixed type and the space Heng hooktop sign k of the solutions of a partial differential equation generalizing the Jacobi equation for the infinitesimal automorphisms of the connection. It is shown that the spaces Heng hooktop signk are finite-dimensional and form a graduated Lie algebra η = ⊕k=0∞ Heng hooktop signk. These algebras are classified in the case of one-dimensional manifolds. It is proved that if the geodesic vector field is complete, then so are the automorphisms corresponding to covariant constant fields of type (1, 1).
AB - We study the structure of those vector fields on the tangent bundle of an arbitrary smooth manifold which commute with the geodesic vector field defined by an affine connection. The study is restricted to polylinear fields generated by a pair of symmetric pseudotensor fields of type (k, 1) and (k + 1, 1), k ≥ 0, defined on the manifold. We establish an isomorphism between the space of infinitesimal automorphisms of fixed type and the space Heng hooktop sign k of the solutions of a partial differential equation generalizing the Jacobi equation for the infinitesimal automorphisms of the connection. It is shown that the spaces Heng hooktop signk are finite-dimensional and form a graduated Lie algebra η = ⊕k=0∞ Heng hooktop signk. These algebras are classified in the case of one-dimensional manifolds. It is proved that if the geodesic vector field is complete, then so are the automorphisms corresponding to covariant constant fields of type (1, 1).
UR - http://www.scopus.com/inward/record.url?scp=54749129982&partnerID=8YFLogxK
M3 - статья
AN - SCOPUS:54749129982
VL - 91
SP - 3476
EP - 3491
JO - Journal of Mathematical Sciences
JF - Journal of Mathematical Sciences
SN - 1072-3374
IS - 6
ER -
ID: 9168733