Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

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



On nullity distributions

Author: Sin Leng Tan
Journal: Trans. Amer. Math. Soc. 223 (1976), 323-335
MSC: Primary 58A30; Secondary 53C05
MathSciNet review: 0423393
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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

  • 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
  • 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
  • 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 Nat. Recherche Sci., 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

Keywords: Affine manifolds, nullity distributions, symmetric spaces, partial integrability
Article copyright: © Copyright 1976 American Mathematical Society