On the interdependency of the Gauss-Codazzi-Ricci equations of local isometric embedding

Hubert F. Goenner

doi:10.1007/bf00770733

On the interdependency of the Gauss-Codazzi-Ricci equations of local isometric embedding

General Relativity and Gravitation ◽

10.1007/bf00770733 ◽

1977 ◽

Vol 8 (2) ◽

pp. 139-145 ◽

Cited By ~ 10

Author(s):

Hubert F. Goenner

Keyword(s):

Isometric Embedding ◽

Local Isometric Embedding

The local isometric embedding inR3 of two-dimensional riemannian manifolds with gaussian curvature changing sign cleanly

Communications on Pure and Applied Mathematics ◽

10.1002/cpa.3160390607 ◽

1986 ◽

Vol 39 (6) ◽

pp. 867-887 ◽

Cited By ~ 41

Author(s):

Chang-Shou Lin

Keyword(s):

Riemannian Manifolds ◽

Gaussian Curvature ◽

Isometric Embedding ◽

Two Dimensional ◽

Local Isometric Embedding

Local isometric embedding of two dimensional Riemannian manifolds into $r^3 $ with nonpositive Gaussian curvature

Proceedings of the Japan Academy Series A Mathematical Sciences ◽

10.3792/pjaa.61.211 ◽

1985 ◽

Vol 61 (7) ◽

pp. 211-212 ◽

Cited By ~ 2

Author(s):

Gen Nakamura

Keyword(s):

Riemannian Manifolds ◽

Gaussian Curvature ◽

Isometric Embedding ◽

Two Dimensional ◽

Local Isometric Embedding

The local isometric embedding in $\mathbf{R}^3$ of 2-dimensional Riemannian manifolds with nonnegative curvature

Journal of Differential Geometry ◽

10.4310/jdg/1214439563 ◽

1985 ◽

Vol 21 (2) ◽

pp. 213-230 ◽

Cited By ~ 29

Author(s):

Chang Shou Lin

Keyword(s):

Riemannian Manifolds ◽

Isometric Embedding ◽

Nonnegative Curvature ◽

Local Isometric Embedding

On the local isometric embedding in ℝ3of surfaces with zero sets of Gaussian curvature forming cusp domains

Communications in Partial Differential Equations ◽

10.1080/03605302.2016.1227336 ◽

2016 ◽

Vol 41 (10) ◽

pp. 1553-1592 ◽

Cited By ~ 1

Author(s):

Tsung-Yin Lin

Keyword(s):

Gaussian Curvature ◽

Isometric Embedding ◽

Zero Sets ◽

Local Isometric Embedding

Local isometric embedding of two-dimensional Riemannian metrics under geometric initial conditions

Analysis ◽

10.1524/anly.2009.1012 ◽

2009 ◽

Vol 29 (2) ◽

Cited By ~ 1

Author(s):

Matthias Bergner

Keyword(s):

Isometric Embedding ◽

Initial Conditions ◽

Riemannian Metrics ◽

Two Dimensional ◽

Local Isometric Embedding

Local Isometric Embedding of Surfaces with Nonpositive Gaussian Curvature

Journal of Differential Geometry ◽

10.4310/jdg/1090426772 ◽

2003 ◽

Vol 63 (3) ◽

pp. 475-520 ◽

Cited By ~ 17

Author(s):

Qing Han ◽

Jia-Xing Hong ◽

Chang-Shou Lin

Keyword(s):

Gaussian Curvature ◽

Isometric Embedding ◽

Local Isometric Embedding

Local isometric embedding of four-dimensional Riemannian manifolds

Exact Solutions of Einstein's Field Equations ◽

10.1017/cbo9780511535185.039 ◽

2003 ◽

pp. 580-604

Keyword(s):

Riemannian Manifolds ◽

Isometric Embedding ◽

Local Isometric Embedding

On the local isometric embedding in $\mathbb{R}^{3}$ of surfaces with Gaussian curvature of mixed sign

Communications in Analysis and Geometry ◽

10.4310/cag.2010.v18.n4.a2 ◽

2010 ◽

Vol 18 (4) ◽

pp. 649-704 ◽

Cited By ~ 9

Author(s):

Qing Han ◽

Marcus Khuri

Keyword(s):

Gaussian Curvature ◽

Isometric Embedding ◽

Local Isometric Embedding

Local Isometric Embedding of Two Dimensional Riemannian Manifolds into $\mathbf{R}^3$ with Nonpositive Gaussian Curvature

Tokyo Journal of Mathematics ◽

10.3836/tjm/1270141807 ◽

1987 ◽

Vol 10 (1) ◽

pp. 241-257 ◽

Cited By ~ 3

Author(s):

Gen NAKAMURA

Keyword(s):

Riemannian Manifolds ◽

Gaussian Curvature ◽

Isometric Embedding ◽

Two Dimensional ◽

Local Isometric Embedding

On the local isometric embedding of trapped surfaces into three-dimensional Riemannian manifolds

Classical and Quantum Gravity ◽

10.1088/1361-6382/aadb39 ◽

2018 ◽

Vol 35 (19) ◽

pp. 195003

Author(s):

Donato Bini ◽

Giampiero Esposito

Keyword(s):

Riemannian Manifolds ◽

Isometric Embedding ◽

Three Dimensional ◽

Trapped Surfaces ◽

Local Isometric Embedding