Open AccessTOTALLY UMBILICAL CR-SUBMANIFOLDS OF A NEARLY KAEHLER MANIFOLD
Author(s) -
S. H. Kon,
Sin-Leng Tan
Publication year - 1996
Publication title -
tamkang journal of mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.324
H-Index - 18
eISSN - 0049-2930
pISSN - 2073-9826
DOI - 10.5556/j.tkjm.27.1996.4352
Subject(s) - submanifold , mathematics , totally geodesic , kähler manifold , manifold (fluid mechanics) , pure mathematics , mathematical analysis , mechanical engineering , engineering
The geometry of a CR-submanifold in a Kaehler manifold has been extensively studied. B.Y . Chen has classified the totally umbilical CR-submanifolds of a Kaehler manifold and showed that they are either totally geodesic, or totally real or dim$(D^{\perp}) =1$. In this paper we show that such a result is also true in a nearly Kaehler manifold.