Dirac reduction of the hamiltonian operator? IJd/dx to a submanifold of euclidean space with flat normal connection

1992 ◽  
Vol 26 (4) ◽  
pp. 298-300 ◽  
Author(s):  
E. V. Ferapontov
Keyword(s):  
Euclidean Space ◽  
Hamiltonian Operator ◽  
Normal Connection ◽  
Flat Normal Connection

scholarly journals Isometric Immersions of Constant Mean Curvature and Triviality of the Normal Connection

1972 ◽  
Vol 45 ◽  
pp. 139-165 ◽  
Author(s):  
Joseph Erbacher
Keyword(s):  
Euclidean Space ◽  
Scalar Curvature ◽  
Mean Curvature ◽  
Additional Assumption ◽  
Constant Mean Curvature ◽  
Constant Scalar Curvature ◽  
Normal Connection ◽  
Isometric Immersions ◽  
The Mean ◽  
Negative Sectional Curvature

In a recent paper [2] Nomizu and Smyth have determined the hypersurfaces Mn of non-negative sectional curvature iso-metrically immersed in the Euclidean space Rn+1 or the sphere Sn+1 with constant mean curvature under the additional assumption that the scalar curvature of Mn is constant. This additional assumption is automatically satisfied if Mn is compact. In this paper we extend these results to codimension p isometric immersions. We determine the n-dimensional submanifolds Mn of non-negative sectional curvature isometrically immersed in the Euclidean Space Rn+P or the sphere Sn+P with constant mean curvature under the additional assumptions that Mn has constant scalar curvature and the curvature tensor of the connection in the normal bundle is zero. By constant mean curvature we mean that the mean curvature normal is paral lel with respect to the connection in the normal bundle. The assumption that Mn has constant scalar curvature is automatically satisfied if Mn is compact. The assumption on the normal connection is automatically sa tisfied if p = 2 and the mean curvature normal is not zero.

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 Anti-invariant submanifolds with flat normal connection

1978 ◽  
Vol 13 (4) ◽  
pp. 577-588 ◽  
Author(s):  
Kentaro Yano ◽  
Masahiro Kon ◽  
Ikuo Ishihara
Keyword(s):  
Normal Connection ◽  
Flat Normal Connection ◽  
Invariant Submanifolds
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