Infinitesimal conditions for the equivariance of morphisms of fibered manifolds

Author:
Yvette Kosmann-Schwarzbach

Journal:
Proc. Amer. Math. Soc. **77** (1979), 374-380

MSC:
Primary 53C10; Secondary 58H05

MathSciNet review:
545599

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Abstract: We generalize the usual definition of the Lie derivative to the case of a morphism between fibered manifolds which does not necessarily preserve the base. We prove that the vanishing of the Lie derivatives is a necessary and sufficient condition for the equivariance of a morphism of fibered manifolds under the action of a connected Lie group.

**[1]**Nicolaas H. Kuiper and Kentaro Yano,*On geometric objects and Lie groups of transformations*, Nederl. Akad. Wetensch. Proc. Ser. A. 58 = Indag. Math.**17**(1955), 411–420. MR**0074048****[2]**Albert Nijenhuis,*Geometric aspects of formal differential operations on tensors fields*, Proc. Internat. Congress Math. 1958, Cambridge Univ. Press, New York, 1960, pp. 463–469. MR**0170293****[3]**-,*Natural bundles and their general properties*, Differential Geometry, in honor of K. Yano, edited by S. Kobayashi, M. Obata and T. Takahashi, Kinokuniya, Tokyo, 1972, pp. 317-334.**[4]**Sarah E. Salvioli,*On the theory of geometric objects*, J. Differential Geometry**7**(1972), 257–278. MR**0320922**

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DOI:
http://dx.doi.org/10.1090/S0002-9939-1979-0545599-9

Keywords:
Lie group of transformations,
Lie derivative,
morphism of fibered manifolds,
equivariant morphism,
geometric objects,
natural bundles

Article copyright:
© Copyright 1979
American Mathematical Society