Skip to Main Content

Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality 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 1.43.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

On nullity distributions
HTML articles powered by AMS MathViewer

by Sin Leng Tan PDF
Trans. Amer. Math. Soc. 223 (1976), 323-335 Request permission

Abstract:

The nullity concept of Riemannian manifolds is extended to affine manifolds. Results obtained by Chern and Kuiper and Maltz on Riemannian manifolds are generalized to affine manifolds. A structure theorem for affine symmetric spaces is obtained. Finally, the nullity concept is generalized to study the partial integrability of certain geometric structures.
References
  • Shiing-shen Chern and Nicolaas H. Kuiper, Some theorems on the isometric imbedding of compact Riemann manifolds in euclidean space, Ann. of Math. (2) 56 (1952), 422–430. MR 50962, DOI 10.2307/1969650
  • Sigurđur Helgason, Differential geometry and symmetric spaces, Pure and Applied Mathematics, Vol. XII, Academic Press, New York-London, 1962. MR 0145455
  • Franz W. Kamber and Philippe Tondeur, Characteristic invariants of foliated bundles, Manuscripta Math. 11 (1974), 51–89. MR 334237, DOI 10.1007/BF01189091
  • Shoshichi Kobayashi and Katsumi Nomizu, Foundations of differential geometry. Vol. I, Wiley Classics Library, John Wiley & Sons, Inc., New York, 1996. Reprint of the 1963 original; A Wiley-Interscience Publication. MR 1393940
  • Robert Maltz, The nullity spaces of the curvature operator, Topologie et Géométrie Différentielle, Vol. 8, Centre National de la Recherche Scientifique, Paris, 1966, pp. 20. MR 0210045
  • Robert Maltz, The nullity spaces of curvature-like tensors, J. Differential Geometry 7 (1972), 519–523. MR 322740
  • J. S. Pasternack, Topological obstructions to integrability and the Riemannian geometry of smooth foliations, Thesis, Princeton Univ., 1970. S. L. Tan, Nullity and generalized characteristic classes of differentiable manifolds, Thesis, Univ. of Illinois, 1974.
Similar Articles
  • Retrieve articles in Transactions of the American Mathematical Society with MSC: 58A30, 53C05
  • Retrieve articles in all journals with MSC: 58A30, 53C05
Additional Information
  • © Copyright 1976 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 223 (1976), 323-335
  • MSC: Primary 58A30; Secondary 53C05
  • DOI: https://doi.org/10.1090/S0002-9947-1976-0423393-9
  • MathSciNet review: 0423393