Complete and Stable O(p+1)×O(q+1)-Invariant Hypersurfaces with Zero Scalar Curvature in Euclidean Space ℝ p+q+2

2006 ◽  
Vol 29 (3) ◽  
pp. 221-240 ◽  
Author(s):  
Jocelino Sato ◽  
Vicente Francisco De Souza Neto
Keyword(s):  
Euclidean Space ◽  
Scalar Curvature ◽  
Zero Scalar Curvature

scholarly journals Stable hypersurfaces with zero scalar curvature in Euclidean space

2016 ◽  
Vol 54 (2) ◽  
pp. 233-241
Author(s):  
Hilário Alencar ◽  
Manfredo Carmo ◽  
Gregório Silva Neto
Keyword(s):  
Euclidean Space ◽  
Scalar Curvature ◽  
Zero Scalar Curvature

scholarly journals Complete hypersurfaces in cylinders

1989 ◽  
Vol 46 (2) ◽  
pp. 313-318
Author(s):  
Thomas Hasanis
Keyword(s):  
Euclidean Space ◽  
Scalar Curvature ◽  
Sectional Curvature ◽  
Positive Scalar Curvature ◽  
Positive Scalar ◽  
Coordinate Functions ◽  
Bounded Below ◽  
Complete Hypersurfaces

AbstractWe consider the extent of certain complete hypersurfaces of Euclidean space. We prove that every complete hypersurface in En+1 with sectional curvature bounded below and non-positive scalar curvature has at least (n − 1) unbounded coordinate functions.

Two-ended hypersurfaces with zero scalar curvature

1999 ◽  
Vol 48 (3) ◽  
pp. 0-0 ◽  
Author(s):  
Jorge Hounie ◽  
Maria Luiza Leite
Keyword(s):  
Scalar Curvature ◽  
Zero Scalar Curvature

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.

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