An equivalence theorem for submanifolds of higher codimensions

• Autorzy: Paweł Witowicz
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

submanifold; affine immersion; normal bundle

Kategorie tematyczne

• 53C40: Global submanifolds

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Annales Polonici Mathematici
• Rocznik: 1994-1995
• Tom: 60
• Numer: 3
• Strony: 211-219

Daty

wydano

1995

otrzymano

1993-07-05

poprawiono

1994-04-08

Twórcy

autor

Paweł Witowicz

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

Bibliografia

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