scholarly journals Cut locus of a separating fractal set in a Riemannian manifold

1998 ◽  
Vol 50 (4) ◽  
pp. 455-467
Author(s):  
Hyeong In Choi ◽  
Doo Seok Lee ◽  
Joung-Hahn Yoon
Keyword(s):  
Riemannian Manifold ◽  
Cut Locus ◽  
Fractal Set

scholarly journals The dimension of a cut locus on a smooth Riemannian manifold

1998 ◽  
Vol 50 (4) ◽  
pp. 571-575 ◽  
Author(s):  
Jin-ichi Itoh ◽  
Minoru Tanaka
Keyword(s):  
Riemannian Manifold ◽  
Cut Locus

Golden Riemannian structures on the tangent bundle with g-natural metrics

Filomat ◽  
2019 ◽  
Vol 33 (8) ◽  
pp. 2543-2554
Author(s):  
E. Peyghan ◽  
F. Firuzi ◽  
U.C. De
Keyword(s):  
Riemannian Manifold ◽  
Tangent Bundle ◽  
Riemannian Metric

Starting from the g-natural Riemannian metric G on the tangent bundle TM of a Riemannian manifold (M,g), we construct a family of the Golden Riemannian structures ? on the tangent bundle (TM,G). Then we investigate the integrability of such Golden Riemannian structures on the tangent bundle TM and show that there is a direct correlation between the locally decomposable property of (TM,?,G) and the locally flatness of manifold (M,g).

Spacetime symmetries

2018 ◽  
Author(s):  
Michael Kachelriess
Keyword(s):  
Riemannian Manifold ◽  
Conservation Laws ◽  
Vector Fields ◽  
Killing Vector ◽  
Geodesic Equation ◽  
Spacetime Symmetries ◽  
Tensor Fields ◽  
Killing Vector Fields ◽  
Covariant Derivatives ◽  
Killing Equation

This chapter introduces tensor fields, covariant derivatives and the geodesic equation on a (pseudo-) Riemannian manifold. It discusses how symmetries of a general space-time can be found from the Killing equation, and how the existence of Killing vector fields is connected to global conservation laws.

Practical Computation of the Cut Locus on Discrete Surfaces

2021 ◽  
Vol 40 (5) ◽  
pp. 261-273
Author(s):  
C. Mancinelli ◽  
M. Livesu ◽  
E. Puppo
Keyword(s):  
Cut Locus ◽  
Practical Computation ◽  
Discrete Surfaces
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