In the first section of the paper we study some properties of oriented volumes of wave fronts propagating in spaces of constant curvature. In the second section, we generalize to an arbitrary isometric action of a Lie group on a Riemannian manifold the following principle: an extra pression inside of a ball does not move it.
@article{bwmeta1.element.bwnjournal-article-bcpv50z1p11bwm,
author = {Anisov, Serge\u\i },
title = {Integral formulas related to wave fronts},
journal = {Banach Center Publications},
volume = {50},
year = {1999},
pages = {11-17},
zbl = {0959.53041},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-bcpv50z1p11bwm}
}
Anisov, Sergeĭ. Integral formulas related to wave fronts. Banach Center Publications, Tome 50 (1999) pp. 11-17. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-bcpv50z1p11bwm/
[000] [1] S. S. Anisov, The 'area-length' duality and the characteristic 2-chain (in Russian), Mat. Zametki 58:3 (1995), 445-446; English transl.: Math. Notes 58 (1995), 983-984. | Zbl 0872.53002
[001] [2] V. I. Arnol'd, Singularities of ray systems (in Russian), Uspekhi Mat. Nauk 38:2 (1983), 77-147; English transl.: Russian Math. Surveys 38:2 (1983), 87-176.
[002] [3] V. I. Arnol'd, Mathematical Methods of Classical Mechanics, second ed., Springer, New York, 1989.
[003] [4] V. I. Arnol'd, The geometry of spherical curves and the algebra of quaternions (in Russian), Uspekhi Mat. Nauk 50:1 (1995), 3-68; English transl.: Russian Math. Surveys 50:1 (1995), 1-68.
[004] [5] A. Gray, Tubes, Addison-Wesley, Redwood City, 1990.
[005] [6] J. Milnor, Morse Theory, Ann. of Math. Stud. 51, Princeton Univ. Press, Princeton, 1963.