On nullity distributions

Tan, Sin Leng

doi:10.1090/S0002-9947-1976-0423393-9

On nullity distributions
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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

Topological obstructions to integrability and the Riemannian geometry of smooth foliations

Nullity and generalized characteristic classes of differentiable manifolds