Isometric immersions of two-dimensional Riemann manifolds in Pseudo-Euclidean space

1984 ◽  
Vol 36 (3) ◽  
pp. 721-725 ◽  
Author(s):  
B. E. Kantor ◽  
S. A. Frangulov
Keyword(s):  
Euclidean Space ◽  
Two Dimensional ◽  
Isometric Immersions ◽  
Riemann Manifolds

An asymptotic analysis for Hamilton–Jacobi equations with large Hamiltonian drift terms

2017 ◽  
Vol 0 (0) ◽  
Author(s):  
Taiga Kumagai
Keyword(s):  
Asymptotic Behavior ◽  
Euclidean Space ◽  
Asymptotic Analysis ◽  
Open Subset ◽  
Dimensional Euclidean Space ◽  
Asymptotic Behavior Of Solutions ◽  
Two Dimensional ◽  
Jacobi Equations ◽  
Drift Terms

AbstractWe investigate the asymptotic behavior of solutions of Hamilton–Jacobi equations with large Hamiltonian drift terms in an open subset of the two-dimensional Euclidean space. The drift is given by

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.

ON EUCLIDEAN G-MANIFOLDS WHICH HAVE TWO DIMENSIONAL ORBIT SPACES

2011 ◽  
Vol 22 (03) ◽  
pp. 399-406
Author(s):  
R. MIRZAIE
Keyword(s):  
Euclidean Space ◽  
Half Plane ◽  
Lie Group ◽  
Orbit Space ◽  
Two Dimensional ◽  
Orbit Spaces ◽  
Group Of Isometries ◽  
Connected Lie Group

We show that the orbit space of Euclidean space, under the action of a closed and connected Lie group of isometries is homeomorphic to a plane or closed half-plane, if the action is of cohomogeneity two.

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