Conformally flat submanifolds
Jean-Marie Morvan; Georges Zafindratafa
Annales de la Faculté des sciences de Toulouse : Mathématiques (1986-1987)
- Volume: 8, Issue: 3, page 331-348
- ISSN: 0240-2963
Access Full Article
topHow to cite
topMorvan, Jean-Marie, and Zafindratafa, Georges. "Conformally flat submanifolds." Annales de la Faculté des sciences de Toulouse : Mathématiques 8.3 (1986-1987): 331-348. <http://eudml.org/doc/73207>.
@article{Morvan1986-1987,
author = {Morvan, Jean-Marie, Zafindratafa, Georges},
journal = {Annales de la Faculté des sciences de Toulouse : Mathématiques},
keywords = {parallel second fundamental form; conformally flat submanifold},
language = {eng},
number = {3},
pages = {331-348},
publisher = {UNIVERSITE PAUL SABATIER},
title = {Conformally flat submanifolds},
url = {http://eudml.org/doc/73207},
volume = {8},
year = {1986-1987},
}
TY - JOUR
AU - Morvan, Jean-Marie
AU - Zafindratafa, Georges
TI - Conformally flat submanifolds
JO - Annales de la Faculté des sciences de Toulouse : Mathématiques
PY - 1986-1987
PB - UNIVERSITE PAUL SABATIER
VL - 8
IS - 3
SP - 331
EP - 348
LA - eng
KW - parallel second fundamental form; conformally flat submanifold
UR - http://eudml.org/doc/73207
ER -
References
top- [Ca 1] Cartan ( E.). — La deformation des hypersurfaces dans l'espace conforme réel à n > 5 dimensions, Bull. Soc. Math. France, t. 45, 1917, p. 65-99. MR4519JFM46.1129.02
- [Ca 2] Cartan ( E.). - Sur les variétés de courbure constante d'un espace euclidien ou non-euclidien, Bull. Soc. Math. France, t. 47, 1919, p. 125-160. Zbl47.0692.03JFM47.0692.03
- [Ch] Chen ( B.Y.). - Geometry of submanifolds. - New-York, M. Dekker1973. Zbl0262.53036MR353212
- [Ch-Ve] Chen ( B.Y.) and Verstraelen ( L.). — A characterisation of totally quasiumbilical submanifolds and its applications, Bul. Un. Mat. Ital., t. (5),14.A, 1977, p. 634. Zbl0365.53007MR478041
- [Ch-Ya 1] Chen ( B.Y.) and Yano K. — Special quasi-umbilical hypersurfaces and locus of sphere, Atti Ac. Naz. Lincei, serie VIII, Vol. L III, t. 3.4, 1972. Zbl0265.53018MR346667
- [Ch-Ya 2] Chen ( B.Y.) and Yano ( K.). — Sous-variétés localement conformes à un espace euclidien, C.R. Acad. Sci.Paris, série A, t. 273, 1972. Zbl0236.53051MR388284
- [Do-Da] Do Carmo ( M.) and Dajczer ( M.). — General conformally flat hypersurfaces of Rn+1. — Preprint.
- [Do-Da-Me] Do Carmo and Dajczer ( M.) and Mercury ( F.). — Compact conformally flat hypersurfaces, Ann. Acad. Brasil. Ciênc., t. 55, 1983'n°2, p. 155-157. Zbl0518.53007MR719927
- [Ep] Epstein ( D.B.A.). — Foliations with all leaves compact, Ann. Inst. Fourier, t. 26, 1, 1976, p. 265-282. Zbl0313.57017MR420652
- [Ko-No] Kobayashi ( S.) and Nomizu ( K.).- Foundations of differential geometry I,II, Wiley Interscience, 1963 and 1969, New-York.
- [La] Lafontaine ( J.). — Remarques sur les variétés conformément plates, Math. Ann., t. 259, 1982, p. 313-319. Zbl0469.53036MR661199
- [Moo 1] Moore ( J.D.). - Isometric immersions of riemannian products, J. Diff. Geom., t. 5, 1971, p. 159-168. Zbl0213.23804MR307128
- [Moo 2] Moore ( J.D.).- Isometric immersions of space forms in space forms, Pacific Journal of Math., t. 40, 1, 1972. Zbl0238.53033MR305312
- [Moo 3] Moore ( J.D.). - Conformally flat submanifolds of euclidian space, Math. Ann., t. 225, 1977185'97. Zbl0322.53027MR431046
- [Mo-Mo] Moore ( J.D.) and Morvan ( J.M.). — Sous-variétés conformément plates de codimension quatre, C.R. Acad. Sci.Paris, t. 287, série A, 1978, p. 655-657. Zbl0396.53030MR514549
- [Mor 2] Morvan ( J.M.).-Some topological properties of totally quasi-umbilical submanifolds, Simon Stevin, t. 54, 1980, n°1, p. 11-25. Zbl0474.53053MR572926
- [Ree] Reeb ( G.). — Sur certaines propriétés topologiques des variétés feuilletées, Act. Sci. Ind., t. 1183, 1952, p. 91-154, 157-158. Zbl0049.12602MR55692
- [Rec 1] Reckziegel ( H.). — Krümmungsflächen von isometrischen Immersionnen in Räume konstanter Krümmung, Math. Ann., t. 223, 1976, p. 169-181. Zbl0319.53042MR425846
- [Rec 2] Reckziegel ( H.). - Completness of curvature surfaces of an isometric immersion, J. Diff. Geom., t. 14, 1979, p. 7-20. Zbl0411.53042MR577875
- [Za] Zafindratafa ( G.).- Sous-variétés conformément plates d'un espace EuclidienThèse de 3ème cycle. Université d'Avignon. France.
NotesEmbed ?
topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.