FLAT TOTALLY-REAL SUBMANIFOLDS OF CP(N) AND THE SYMMETRICAL GENERALIZED WAVE-EQUATION

Authors
DAJCZER M TOJEIRO R
Citation
M. Dajczer et R. Tojeiro, FLAT TOTALLY-REAL SUBMANIFOLDS OF CP(N) AND THE SYMMETRICAL GENERALIZED WAVE-EQUATION, Tohoku Mathematical Journal, 47(1), 1995, pp. 117-123
Citations number
15
Categorie Soggetti
Mathematics, General",Mathematics
Journal title
Tohoku Mathematical Journal → ACNP
ISSN journal
00408735
Volume
47
Issue
1
Year of publication
1995
Pages
117 - 123
Database
ISI
SICI code
0040-8735(1995)47:1<117:FTSOCA>2.0.ZU;2-M
Abstract
In this paper we show that the projection of the Hopf fibration establ ishes a one-to-one correspondence between the set of symmetric flat su bmanifolds in Euclidean sphere and the set of totally real flat subman ifolds in complex projective space with the same codimension. We also show that any complete totally real submanifold in complex projective space with mean curvature of constant length and equal dimension and c odimension is a flat torus.