Integral Geometry of Tensor Fields

1994 ◽  
Author(s):  
V. A. Sharafutdinov
Keyword(s):  
Integral Geometry ◽  
Tensor Fields

Full reconstruction of a vector field from restricted Doppler and first integral moment transforms in ℝn

2020 ◽  
Vol 28 (2) ◽  
pp. 173-184 ◽  
Author(s):  
Rohit Kumar Mishra
Keyword(s):  
Vector Field ◽  
Integral Geometry ◽  
Tensor Field ◽  
Vector Fields ◽  
First Integral ◽  
Tensor Fields ◽  
Line Complex ◽  
Full Reconstruction ◽  
Ill Posed ◽  
Fixed Curve

AbstractWe show that a vector field in {\mathbb{R}^{n}} can be reconstructed uniquely from the knowledge of restricted Doppler and first integral moment transforms. The line complex we consider consists of all lines passing through a fixed curve {\gamma\subset\mathbb{R}^{n}}. The question of reconstruction of a symmetric m-tensor field from the knowledge of the first {m+1} integral moments was posed by Sharafutdinov [Integral Geometry of Tensor Fields, Inverse Ill-posed Probl. Ser. 1, De Gruyter, Berlin, 1994, p. 78]. In this work, we provide an answer to Sharafutdinov’s question for the case of vector fields from restricted data comprising of the first two integral moment transforms.

Integral geometry of tensor fields on a manifold of negative curvature

1989 ◽  
Vol 29 (3) ◽  
pp. 427-441 ◽  
Author(s):  
L. N. Pestov ◽  
V. A. Sharafutdinov
Keyword(s):  
Integral Geometry ◽  
Negative Curvature ◽  
Tensor Fields

On Horizontal and Complete Lifts of $(1,1)\;$ Tensor Fields F Satisfying ${f(2K+S,S)=0}$

2016 ◽  
Vol 6 (1) ◽  
pp. 143
Author(s):  
Abhishek Singh ◽  
Ramesh Kumar Pandey ◽  
Sachin Khare
Keyword(s):  
Tensor Fields

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.

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