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Some problems of integral geometry on Anosov manifolds

Published online by Cambridge University Press:  16 January 2003

NURLAN S. DAIRBEKOV  and
VLADIMIR A. SHARAFUTDINOV
NURLAN S. DAIRBEKOV
Affiliation:
Sobolev Institute of Mathematics, 4 Koptyug Av., Novosibirsk, 630090, Russia (e-mail: [email protected], [email protected])
VLADIMIR A. SHARAFUTDINOV
Affiliation:
Sobolev Institute of Mathematics, 4 Koptyug Av., Novosibirsk, 630090, Russia (e-mail: [email protected], [email protected])
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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.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 23 , Issue 1 , February 2003 , pp. 59 - 74
Copyright
2003 Cambridge University Press

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