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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

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Almost tangent and cotangent structures in the large
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by G. Thompson and U. Schwardmann PDF
Trans. Amer. Math. Soc. 327 (1991), 313-328 Request permission

Abstract:

We examine some global properties of integrable almost tangent and cotangent manifolds. In particular, we extend several results which essentially characterize tangent and cotangent bundles as, respectively, regular almost tangent and cotangent structures.
References
  • John K. Beem, Proper homothetic maps and fixed points, Lett. Math. Phys. 2 (1977/78), no. 4, 317–320. MR 501280, DOI 10.1007/BF00419621
  • Raoul Bott and Loring W. Tu, Differential forms in algebraic topology, Graduate Texts in Mathematics, vol. 82, Springer-Verlag, New York-Berlin, 1982. MR 658304
  • F. Brickell and R. S. Clark, Integrable almost tangent structures, J. Differential Geometry 9 (1974), 557–563. MR 348666
  • M. R. Bruckheimer, Doctoral thesis, University of Southampton, 1960.
  • R. S. Clark and D. S. Goel, On the geometry of an almost tangent manifold, Tensor (N.S.) 24 (1972), 243–252. MR 326613
  • R. S. Clark and D. S. Goel, Almost cotangent manifolds, J. Differential Geometry 9 (1974), 109–122. MR 365404
  • M. Crampin, Tangent bundle geometry for Lagrangian dynamics, J. Phys. A 16 (1983), no. 16, 3755–3772. MR 727054
  • M. Crampin and G. Thompson, Affine bundles and integrable almost tangent structures, Math. Proc. Cambridge Philos. Soc. 98 (1985), no. 1, 61–71. MR 789719, DOI 10.1017/S0305004100063246
  • M. Crampin and L. A. Ibort, Graded Lie algebras of derivations and Ehresmann connections, J. Math. Pures Appl. (9) 66 (1987), no. 1, 113–125. MR 884816
  • Hermes A. Eliopoulos, Structures presque tangentes sur les variétés différentiables, C. R. Acad. Sci. Paris 255 (1962), 1563–1565 (French). MR 142078
  • Hermes A. Eliopoulos, On the general theory of differentiable manifolds with almost tangent structure, Canad. Math. Bull. 8 (1965), 721–748. MR 193590, DOI 10.4153/CMB-1965-054-5
  • Joseph Grifone, Structure presque-tangente et connexions. I, Ann. Inst. Fourier (Grenoble) 22 (1972), no. 1, 287–334 (French, with English summary). MR 336636
  • Joseph Grifone, Structure presque-tangente et connexions. II, Ann. Inst. Fourier (Grenoble) 22 (1972), no. 3, 291–338. (loose errata) (French, with English summary). MR 341361
  • Victor Guillemin and Shlomo Sternberg, Geometric asymptotics, Mathematical Surveys, No. 14, American Mathematical Society, Providence, R.I., 1977. MR 0516965
  • Victor Guillemin and Shlomo Sternberg, Symplectic techniques in physics, Cambridge University Press, Cambridge, 1984. MR 770935
  • Joseph Klein, Espaces variationnels et mécanique, Ann. Inst. Fourier (Grenoble) 12 (1962), 1–124 (French). MR 215269
  • —, Structures symplectiques ou $J$-symplectiques homogènes sur l’espace tangent, Symposia Math. 14 (1974), 181-192. —, Geometry of sprays. Lagrangian case principle of least curvature, Proc. IUTAM-ISIMM Symposium on Modern Developments in Analytical Mechanics, Torino, 1982.
  • Shoshichi Kobayashi, Transformation groups in differential geometry, Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 70, Springer-Verlag, New York-Heidelberg, 1972. MR 0355886
  • Detlef Laugwitz, Differential and Riemannian geometry, Academic Press, New York-London, 1965. Translated by Fritz Steinhardt. MR 0172184
  • John W. Milnor and James D. Stasheff, Characteristic classes, Annals of Mathematics Studies, No. 76, Princeton University Press, Princeton, N. J.; University of Tokyo Press, Tokyo, 1974. MR 0440554
  • Shlomo Sternberg, Lectures on differential geometry, Prentice-Hall, Inc., Englewood Cliffs, N.J., 1964. MR 0193578
  • G. Thompson, Integrable almost cotangent structures and Legendrian bundles, Math. Proc. Cambridge Philos. Soc. 101 (1987), no. 1, 61–78. MR 877701, DOI 10.1017/S030500410006641X
  • Alan Weinstein, Lectures on symplectic manifolds, Regional Conference Series in Mathematics, No. 29, American Mathematical Society, Providence, R.I., 1977. Expository lectures from the CBMS Regional Conference held at the University of North Carolina, March 8–12, 1976. MR 0464312
  • N. M. J. Woodhouse, Geometric quantization, 2nd ed., Oxford Mathematical Monographs, The Clarendon Press, Oxford University Press, New York, 1992. Oxford Science Publications. MR 1183739
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Additional Information
  • © Copyright 1991 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 327 (1991), 313-328
  • MSC: Primary 53C15; Secondary 53C10
  • DOI: https://doi.org/10.1090/S0002-9947-1991-1012509-X
  • MathSciNet review: 1012509