scholarly journals Conformally flat submanifolds with flat normal bundle

2019 ◽  
Vol 163 (3-4) ◽  
pp. 407-426 ◽  
Author(s):  
M. Dajczer ◽  
C.-R. Onti ◽  
Th. Vlachos
Keyword(s):  
Normal Bundle ◽  
Conformally Flat ◽  
Flat Normal Bundle ◽  
Conformally Flat Submanifolds ◽  
Flat Submanifolds

Submanifolds with Nonparallel First Normal Bundle

1994 ◽  
Vol 37 (3) ◽  
pp. 330-337 ◽  
Author(s):  
Marcos Dajczer ◽  
Ruy Tojeiro
Keyword(s):  
Euclidean Space ◽  
Sectional Curvature ◽  
Normal Bundle ◽  
Second Fundamental Form ◽  
Low Rank ◽  
Geometric Description ◽  
Normal Connection ◽  
Flat Normal Bundle ◽  
The Second Fundamental Form ◽  
Flat Submanifolds

AbstractWe provide a complete local geometric description of submanifolds of spaces with constant sectional curvature where the first normal spaces, that is, the subspaces spanned by the second fundamental form, form a vector subbundle of the normal bundle of low rank which is nonparallel in the normal connection. We also characterize flat submanifolds with flat normal bundle in Euclidean space satisfying the helix property.

scholarly journals Conformally flat submanifolds

1987 ◽  
Vol 8 (3) ◽  
pp. 331-348 ◽  
Author(s):  
Jean-Marie Morvan ◽  
Georges Zafindratafa
Keyword(s):  
Conformally Flat ◽  
Conformally Flat Submanifolds ◽  
Flat Submanifolds

scholarly journals On conformally flat submanifolds

1996 ◽  
Vol 4 (2) ◽  
pp. 261-284 ◽  
Author(s):  
Marcos Dajczer ◽  
Luis A. Florit
Keyword(s):  
Conformally Flat ◽  
Conformally Flat Submanifolds ◽  
Flat Submanifolds
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