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

Invariant tensor fields of dynamical systems with pinched Lyapunov exponents and rigidity of geodesic flows

1989 ◽  
Vol 9 (3) ◽  
pp. 427-432 ◽  
Author(s):  
Renato Feres ◽  
Anatoly Katok
Keyword(s):  
Dynamical Systems ◽  
Lyapunov Exponents ◽  
Riemannian Manifolds ◽  
Negative Curvature ◽  
Geodesic Flows ◽  
Tensor Fields ◽  
Invariant Tensor ◽  
Affine Connections

AbstractWe consider in this note smooth dynamical systems equipped with smooth invariant affine connections and show that, under a pinching condition on the Lyapunov exponents, certain invariant tensor fields are parallel. We then apply this result to a problem of rigidity of geodesic flows for Riemannian manifolds with negative curvature.

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.

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
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