An equivalence theorem for submanifolds of higher codimensions

Paweł Witowicz

Annales Polonici Mathematici (1995)

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

Abstract

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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.

How to cite

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Paweł 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

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  1. [1] C. B. Allendoerfer, Rigidity for spaces of class greater than one, Amer. J. Math. 61 (1939), 633-644. Zbl0021.15803
  2. [2] F. Dillen, Equivalence theorems in affine differential geometry, Geom. Dedicata 32 (1988), 81-92. Zbl0684.53012
  3. [3] S. Kobayashi and K. Nomizu, Foundations of Differential Geometry, Vol. II (Appendix), Wiley, New York, 1969. Zbl0175.48504
  4. [4] K. Nomizu and U. Pinkall, Cubic form theorem for affine immersions, Results in Math. 13 (1988), 338-362. 
  5. [5] B. Opozda, Some equivalence theorems in affine hypersurface theory, Monatsh. Math. 113 (1992), 245-254. Zbl0776.53007
  6. [6] M. Spivak, A Copmprehensive Introduction to Differential Geometry, Vol. 5, Publish or Perish, 1979, 361-369. 

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