Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
   
Mobile Device Pairing
Green Open Access
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

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
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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.


References [Enhancements On Off] (What's this?)

  • [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 (17,528c)
  • [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 (30 #531)
  • [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 (47 #9455)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 53C10, 58H05

Retrieve articles in all journals with MSC: 53C10, 58H05


Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1979-0545599-9
PII: S 0002-9939(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