scholarly journals Gauss Equation And Injectivity Radii For Subspaces in Spaces of Curvature Bounded Above

2006 ◽  
Vol 117 (1) ◽  
pp. 65-84 ◽  
Author(s):  
Stephanie B. Alexander ◽  
Richard L. Bishop
Keyword(s):  
Gauss Equation ◽  
Injectivity Radii

scholarly journals On the solution of a class of second-order quasi-linear PDEs and the Gauss equation

2001 ◽  
Vol 42 (3) ◽  
pp. 312-323
Author(s):  
A. R. Selvaratnam ◽  
M. Vlieg-Hulstman ◽  
B. van-Brunt ◽  
W. D. Halford
Keyword(s):  
Gaussian Curvature ◽  
Gordon Equation ◽  
Second Order ◽  
Bäcklund Transformations ◽  
Coordinate Systems ◽  
Gauss Equation ◽  
Sine Gordon Equation ◽  
Partial Differential ◽  
Metric Tensor ◽  
Backlund Transformations

AbstractGauss' Theorema Egregium produces a partial differential equation which relates the Gaussian curvature K to components of the metric tensor and its derivatives. Well-known partial differential equations (PDEs) such as the Schrödinger equation and the sine-Gordon equation can be derived from Gauss' equation for specific choices of K and coördinate systems. In this paper we consider a class of Bäcklund Transformations which corresponds to coördinate transformations on surfaces with a given Gaussian curvature. These Bäcklund Transformations lead to the construction of solutions to certain classes of non-linear second order PDEs of hyperbolic type by identifying these PDEs as the Gauss equation in some coördinate system. The possibility of solving the Cauchy Problem has also been explored for these classes of equations.

scholarly journals An upper bound for injectivity radii in convex cores

2013 ◽  
Vol 7 (1) ◽  
pp. 109-126 ◽  
Author(s):  
Brian Bowditch
Keyword(s):  
Upper Bound ◽  
Injectivity Radii

scholarly journals Binary Image Segmentation through the Carl Friedrich Gauss Equation

2018 ◽  
Vol 179 (41) ◽  
pp. 1-9
Author(s):  
Oppong-Twum Francis ◽  
Frimpong Twum ◽  
J. B.
Keyword(s):  
Image Segmentation ◽  
Binary Image ◽  
Gauss Equation

scholarly journals Injectivity radii of hyperbolic polyhedra

2001 ◽  
Vol 197 (2) ◽  
pp. 369-382 ◽  
Author(s):  
Joseph D. Masters
Keyword(s):  
Hyperbolic Polyhedra ◽  
Injectivity Radii

scholarly journals Betti numbers and injectivity radii

2009 ◽  
Vol 137 (11) ◽  
pp. 3919-3919 ◽  
Author(s):  
Marc Culler ◽  
Peter B. Shalen
Keyword(s):  
Betti Numbers ◽  
Injectivity Radii

The Gauss Equation in Capillarity

1977 ◽  
Vol 105 (5_6) ◽  
pp. 225-235 ◽  
Author(s):  
Sun-Tak Hwang
Keyword(s):  
Gauss Equation

Real hypersurfaces in complex two-plane Grassmannians with parallel Ricci tensor

2012 ◽  
Vol 142 (6) ◽  
pp. 1309-1324 ◽  
Author(s):  
Young Jin Suh
Keyword(s):  
Curvature Tensor ◽  
Ricci Tensor ◽  
Real Hypersurface ◽  
Real Hypersurfaces ◽  
Gauss Equation ◽  
Full Expression ◽  
New Formula ◽  
Parallel Ricci Tensor

We introduce the full expression of the curvature tensor of a real hypersurface M in complex two-plane Grassmannians G2(ℂm+2) from the Gauss equation. We then derive a new formula for the Ricci tensor of M in G2(ℂm+2). Finally, we prove that there does not exist any Hopf real hypersurface in complex two-plane Grassmannians G2(ℂm+2) with parallel Ricci tensor.

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