On compositions of conformal immersions
HTML articles powered by AMS MathViewer
- by Marcos Dajczer and Enaldo Vergasta PDF
- Proc. Amer. Math. Soc. 118 (1993), 211-215 Request permission
Abstract:
We consider conformal immersions of a manifold ${M^n},\;n \geqslant 6$, into conformally flat manifolds. If the principal curvatures of $f:{M^n} \to N_{cf}^{n + 1}$ have multiplicities at most $n - 4$, we show that any $g:{M^n} \to \tilde N_{cf}^{n + 2}$ can locally be written as $g = \rho \circ f$, where $\rho :N_{cf}^{n + 1} \to \tilde N_{cf}^{n + 2}$ is a conformal immersion.References
- E. Cartan, La déformation des hypersurfaces dans l’espace conforme réel à $n \ge 5$ dimensions, Bull. Soc. Math. France 45 (1917), 57–121 (French). MR 1504762
- Manfredo do Carmo and Marcos Dajczer, Conformal rigidity, Amer. J. Math. 109 (1987), no. 5, 963–985. MR 910359, DOI 10.2307/2374496
- Bang-yen Chen and Kentaro Yano, Umbilical submanifolds with respect to a nonparallel normal direction, J. Differential Geometry 8 (1973), 589–597. MR 341347
- Manfredo do Carmo, Marcos Dajczer, and Francesco Mercuri, Compact conformally flat hypersurfaces, Trans. Amer. Math. Soc. 288 (1985), no. 1, 189–203. MR 773056, DOI 10.1090/S0002-9947-1985-0773056-0
- Marcos Dajczer, Submanifolds and isometric immersions, Mathematics Lecture Series, vol. 13, Publish or Perish, Inc., Houston, TX, 1990. Based on the notes prepared by Mauricio Antonucci, Gilvan Oliveira, Paulo Lima-Filho and Rui Tojeiro. MR 1075013
- Marcos Dajczer and Detlef Gromoll, Isometric deformations of compact Euclidean submanifolds in codimension $2$, Duke Math. J. 79 (1995), no. 3, 605–618. MR 1355178, DOI 10.1215/S0012-7094-95-07915-0
Additional Information
- © Copyright 1993 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 118 (1993), 211-215
- MSC: Primary 53C42; Secondary 53A30
- DOI: https://doi.org/10.1090/S0002-9939-1993-1164141-2
- MathSciNet review: 1164141