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Mat. Zametki, 1976, Volume 19, Issue 2, Pages 247–258 (Mi mz7744)  

Canonical decomposition of projective and affine killing vectors on the tangent bundle

F. I. Kagan

Ivanovo Textile Institute

Abstract: For an affine connection on the tangent bundle $T(M)$ obtained by lifting an affine connection on $M$, the structure of vector fields on $T(M)$ which generate local one-parameter groups of projective and affine collineations is described. On the $T(M)$ of a complete irreducible Riemann manifold, every projective collineation is affine. On the $T(M)$ of a projectively Euclidean space, every affine collineation preserves the fibration of $T(M)$, and on the $T(M)$ of a projectively non-Euclidean space which is maximally homogeneous (in the sense of affine collineations) there exist affine collineations permuting the fibers of $T(M)$.

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English version:
Mathematical Notes, 1976, 19:2, 146–152

Bibliographic databases:

UDC: 513
Received: 25.03.1974

Citation: F. I. Kagan, “Canonical decomposition of projective and affine killing vectors on the tangent bundle”, Mat. Zametki, 19:2 (1976), 247–258; Math. Notes, 19:2 (1976), 146–152

Citation in format AMSBIB
\Bibitem{Kag76}
\by F.~I.~Kagan
\paper Canonical decomposition of projective and affine killing vectors on the tangent bundle
\jour Mat. Zametki
\yr 1976
\vol 19
\issue 2
\pages 247--258
\mathnet{http://mi.mathnet.ru/mz7744}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=417973}
\zmath{https://zbmath.org/?q=an:0327.53021}
\transl
\jour Math. Notes
\yr 1976
\vol 19
\issue 2
\pages 146--152
\crossref{https://doi.org/10.1007/BF01098748}


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