Level sets of scalar Weyl invariants and cohomogeneity
HTML articles powered by AMS MathViewer
- by Sergio Console and Carlos Olmos PDF
- Trans. Amer. Math. Soc. 360 (2008), 629-641 Request permission
Abstract:
We prove that the cohomogeneity of a Riemannian manifold coincides locally with the codimension of the foliation by regular level sets of the scalar Weyl invariants.References
- Peter Dombrowski, On the geometry of the tangent bundle, J. Reine Angew. Math. 210 (1962), 73–88. MR 141050, DOI 10.1515/crll.1962.210.73
- D. B. A. Epstein, Natural tensors on Riemannian manifolds, J. Differential Geometry 10 (1975), no. 4, 631–645. MR 415531
- L. Nicolodi and F. Tricerri, On two theorems of I. M. Singer about homogeneous spaces, Ann. Global Anal. Geom. 8 (1990), no. 2, 193–209. MR 1088511, DOI 10.1007/BF00128003
- Barrett O’Neill, The fundamental equations of a submersion, Michigan Math. J. 13 (1966), 459–469. MR 200865
- Fabio Podestà and Andrea Spiro, Cohomogeneity one manifolds and hypersurfaces of the Euclidean space, Ann. Global Anal. Geom. 13 (1995), no. 2, 169–184. MR 1336212, DOI 10.1007/BF01120332
- Friedbert Prüfer, Franco Tricerri, and Lieven Vanhecke, Curvature invariants, differential operators and local homogeneity, Trans. Amer. Math. Soc. 348 (1996), no. 11, 4643–4652. MR 1363946, DOI 10.1090/S0002-9947-96-01686-8
- I. M. Singer, Infinitesimally homogeneous spaces, Comm. Pure Appl. Math. 13 (1960), 685–697. MR 131248, DOI 10.1002/cpa.3160130408
- Héctor J. Sussmann, Orbits of families of vector fields and integrability of distributions, Trans. Amer. Math. Soc. 180 (1973), 171–188. MR 321133, DOI 10.1090/S0002-9947-1973-0321133-2
Additional Information
- Sergio Console
- Affiliation: Dipartimento di Matematica, Università di Torino, via Carlo Alberto 10, 10123 Torino, Italy
- Email: sergio.console@unito.it
- Carlos Olmos
- Affiliation: FaMAF, Universidad Nacional de Córdoba, Ciudad Universitaria, 5000 Córdoba, Argentina
- MR Author ID: 270951
- Email: olmos@mate.uncor.edu
- Received by editor(s): July 28, 2005
- Published electronically: September 21, 2007
- Additional Notes: The first author was partially supported by GNSAGA of INdAM and MIUR (Italy)
The second author was supported by Universidad Nacional de Córdoba and CONICET, and partially supported by Antorchas, ANCyT, Secyt-UNC, and CIEM - © Copyright 2007
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Trans. Amer. Math. Soc. 360 (2008), 629-641
- MSC (2000): Primary 53C30; Secondary 53C21
- DOI: https://doi.org/10.1090/S0002-9947-07-04529-1
- MathSciNet review: 2346465
Dedicated: To the memory of Aristide Sanini