Ergodic Theory and Dynamical Systems

Table of Contents - 2003 - Volume 23, Issue 01  


Some problems of integral geometry on Anosov manifolds

NURLAN S. DAIRBEKOV a1 and VLADIMIR A. SHARAFUTDINOV a1
a1 Sobolev Institute of Mathematics, 4 Koptyug Av., Novosibirsk, 630090, Russia (e-mail: dair@math.nsc.ru, sharaf@math.nsc.ru)

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.

(Received July 16 1999)
(Revised January 19 2002)