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Article · Ergodic Theory and Dynamical Systems · January 16, 2003

Some problems of integral geometry on Anosov manifolds

N. S. Dairbekov, V. A. Sharafutdinov

Nurlan Dairbekov
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Abstract

In this paper we prove that on an Anosov manifold the space of symmetric m-tensor fields of vanishing energy is finite dimensional modulo the space of potential tensor fields for an arbitrary m and coincides with the latter for m=0 and m=1. For m=2 this question relates to the spectral rigidity problem.

Advanced Differential Geometry ResearchMathematical Dynamics and FractalsGeometric Analysis and Curvature Flowsintegral geometrysymmetric tensor fieldsfinite-dimensional vector spaces

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