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 CMFD, 2012, Volume 46, Pages 141–152 (Mi cmfd234)

On the index formula for an isometric diffeomorphism

A. Yu. Savinab, B. Yu. Sterninab, E. Schroheb

a People's Friendship University of Russia, Moscow, Russia
b Hannover Leibnitz-Universität, Hannover, Germany

Abstract: We give an elementary solution to the problem of the index of elliptic operators associated with shift operator along the trajectories of an isometric diffeomorphism of a smooth closed manifold. This solution is based on index-preserving reduction of the operator under consideration to some elliptic pseudo-differential operator on a higher-dimension manifold and on the application of the Atiyah–Singer formula. The final formula of the index is given in terms of the symbol of the operator on the original manifold.

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English version:
Journal of Mathematical Sciences, 2014, 201:6, 818–829

UDC: 515.168.5+517.956.22

Citation: A. Yu. Savin, B. Yu. Sternin, E. Schrohe, “On the index formula for an isometric diffeomorphism”, Proceedings of the Sixth International Conference on Differential and Functional-Differential Equations (Moscow, August 14–21, 2011). Part 2, CMFD, 46, PFUR, M., 2012, 141–152; Journal of Mathematical Sciences, 201:6 (2014), 818–829

Citation in format AMSBIB
\Bibitem{SavSteSch12} \by A.~Yu.~Savin, B.~Yu.~Sternin, E.~Schrohe \paper On the index formula for an isometric diffeomorphism \inbook Proceedings of the Sixth International Conference on Differential and Functional-Differential Equations (Moscow, August 14--21, 2011). Part~2 \serial CMFD \yr 2012 \vol 46 \pages 141--152 \publ PFUR \publaddr M. \mathnet{http://mi.mathnet.ru/cmfd234} \transl \jour Journal of Mathematical Sciences \yr 2014 \vol 201 \issue 6 \pages 818--829 \crossref{https://doi.org/10.1007/s10958-014-2027-4} \scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84919904838}