# An equivalence theorem for submanifolds of higher codimensions

Annales Polonici Mathematici (1995)

- Volume: 60, Issue: 3, page 211-219
- ISSN: 0066-2216

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topPaweł Witowicz. "An equivalence theorem for submanifolds of higher codimensions." Annales Polonici Mathematici 60.3 (1995): 211-219. <http://eudml.org/doc/262422>.

@article{PawełWitowicz1995,

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.},

author = {Paweł Witowicz},

journal = {Annales Polonici Mathematici},

keywords = {submanifold; affine immersion; normal bundle},

language = {eng},

number = {3},

pages = {211-219},

title = {An equivalence theorem for submanifolds of higher codimensions},

url = {http://eudml.org/doc/262422},

volume = {60},

year = {1995},

}

TY - JOUR

AU - Paweł Witowicz

TI - An equivalence theorem for submanifolds of higher codimensions

JO - Annales Polonici Mathematici

PY - 1995

VL - 60

IS - 3

SP - 211

EP - 219

AB - 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.

LA - eng

KW - submanifold; affine immersion; normal bundle

UR - http://eudml.org/doc/262422

ER -

## References

top- [1] C. B. Allendoerfer, Rigidity for spaces of class greater than one, Amer. J. Math. 61 (1939), 633-644. Zbl0021.15803
- [2] F. Dillen, Equivalence theorems in affine differential geometry, Geom. Dedicata 32 (1988), 81-92. Zbl0684.53012
- [3] S. Kobayashi and K. Nomizu, Foundations of Differential Geometry, Vol. II (Appendix), Wiley, New York, 1969. Zbl0175.48504
- [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. Zbl0776.53007
- [6] M. Spivak, A Copmprehensive Introduction to Differential Geometry, Vol. 5, Publish or Perish, 1979, 361-369.

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