An equivalence theorem for submanifolds of higher codimensions

Paweł Witowicz

ArticleOriginal scientific text

Title

An equivalence theorem for submanifolds of higher codimensions

Authors ¹

Affiliations

Institute of Mathematics, Pedagogical University, W. Pola 2, 35-959 Rzeszów, Poland

Abstract

For a submanifold of

ℝ^{n}

of any codimension the notion of type number is introduced. Under the assumption that the type number is greater than 1 an equivalence theorem is proved.

Keywords

ENG

submanifold, affine immersion, normal bundle

C. B. Allendoerfer, Rigidity for spaces of class greater than one, Amer. J. Math. 61 (1939), 633-644.
F. Dillen, Equivalence theorems in affine differential geometry, Geom. Dedicata 32 (1988), 81-92.
S. Kobayashi and K. Nomizu, Foundations of Differential Geometry, Vol. II (Appendix), Wiley, New York, 1969.
K. Nomizu and U. Pinkall, Cubic form theorem for affine immersions, Results in Math. 13 (1988), 338-362.
B. Opozda, Some equivalence theorems in affine hypersurface theory, Monatsh. Math. 113 (1992), 245-254.
M. Spivak, A Copmprehensive Introduction to Differential Geometry, Vol. 5, Publish or Perish, 1979, 361-369.

Title

An equivalence theorem for submanifolds of higher codimensions

Affiliations

Abstract

Keywords

Bibliography