Conditions on the projective curvature tensor of hypersurfaces in euclidian space

J. Deprez; F. Dillen; P. Verheyen; L. Verstraelen

Annales de la Faculté des sciences de Toulouse : Mathématiques (1985)

  • Volume: 7, Issue: 3-4, page 229-249
  • ISSN: 0240-2963

How to cite

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Deprez, J., et al. "Conditions on the projective curvature tensor of hypersurfaces in euclidian space." Annales de la Faculté des sciences de Toulouse : Mathématiques 7.3-4 (1985): 229-249. <http://eudml.org/doc/73181>.

@article{Deprez1985,
author = {Deprez, J., Dillen, F., Verheyen, P., Verstraelen, L.},
journal = {Annales de la Faculté des sciences de Toulouse : Mathématiques},
keywords = {hypersurfaces; projective curvature tensor; hypersurfaces of revolution; catenoid},
language = {eng},
number = {3-4},
pages = {229-249},
publisher = {UNIVERSITE PAUL SABATIER},
title = {Conditions on the projective curvature tensor of hypersurfaces in euclidian space},
url = {http://eudml.org/doc/73181},
volume = {7},
year = {1985},
}

TY - JOUR
AU - Deprez, J.
AU - Dillen, F.
AU - Verheyen, P.
AU - Verstraelen, L.
TI - Conditions on the projective curvature tensor of hypersurfaces in euclidian space
JO - Annales de la Faculté des sciences de Toulouse : Mathématiques
PY - 1985
PB - UNIVERSITE PAUL SABATIER
VL - 7
IS - 3-4
SP - 229
EP - 249
LA - eng
KW - hypersurfaces; projective curvature tensor; hypersurfaces of revolution; catenoid
UR - http://eudml.org/doc/73181
ER -

References

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  1. [1] D.E. Blair. «On a generalization of the catenoid». Can. J. Math., Vol. XXVI I, n° 2, 1975, pp. 231-236. Zbl0307.53003MR380637
  2. [2] B.Y. Chen. «Geometry of submanifolds». Marcel Dekker, New York, 1973. Zbl0262.53036MR353212
  3. [3] J. Deprez. «Semi-parallel hypersurfaces». To appear in Rend. Sem. Mat. Univ. Politecnico Torino. Zbl0616.53018MR906021
  4. [4] J. Deprez, P. Verheyen and L. Verstraelen. «Characterizations of conformally flat hypersurfaces». Czechoslovak Math. J.35 (110) 1985. Zbl0586.53001MR779341
  5. [5] P. Hartman and L. Nirenberg. «On spherical image maps whose Jacobians do not change sign». Amer. J. Math.8 (1959), 901-920. Zbl0094.16303MR126812
  6. [6] S. Kobayashi and K. Nomizu. «Foundations of differential geometry I». Interscience Publ.1963, London. Zbl0119.37502MR152974
  7. [7] K. Nomizu. « On hypersurfaces satisfying a certain condition on the curvature tensor». Tôhoku Math. J.20 (1968), 46-59. Zbl0174.53301MR226549
  8. [8] P.J. Ryan. «Homogeneity and some curvature conditions for hypersurfaces». Tôhoku Math. J.21 (1969), 363-388. Zbl0185.49904MR253243
  9. [9] Z.I. Szabo. «Structure theorems on Riemannian spaces satisfying R(X,Y) R = 0. I. The local version». J. Differential Geometry17 (1982), 531-582. Zbl0508.53025MR683165

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