A finiteness theorem for Riemannian submersions

• Autorzy: Paweł G. Walczak
• Języki publikacji: EN

Abstrakty

EN

Given some geometric bounds for the base space and the fibres, there is a finite number of conjugacy classes of Riemannian submersions between compact Riemannian manifolds.

Słowa kluczowe

EN

Riemannian foliation; Riemannian submersion; geometry bounds; finiteness

Kategorie tematyczne

• 53C20: Global Riemannian geometry, including pinching
• 53C12: Foliations (differential geometric aspects)
• 57R30: Foliations; geometric theory

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Annales Polonici Mathematici
• Rocznik: 1992
• Tom: 57
• Numer: 3
• Strony: 283-290

Daty

wydano

1992

otrzymano

1992-01-02

Twórcy

autor

Paweł G. Walczak

• Institute of Mathematics, University of Łódź, Banacha 22, 90-238 Łódź, Poland

Bibliografia

• [A] M. T. Anderson, Convergence and rigidity of manifolds under Ricci curvature bounds, Invent. Math. 102 (1990), 429-445.
• [AC] M. T. Anderson and J. Cheeger, Diffeomorphism finiteness for manifolds with Ricci curvature and $L^{n/2}$-norm of curvature bounded, Geom. Funct. Anal. 1 (1991), 231-252.
• [BK] P. Buser and H. Karcher, Gromov's almost flat manifolds, Astérisque 81 (1981), 1-148.
• [C] J. Cheeger, Finiteness theorems for Riemannian manifolds, Amer. J. Math. 92 (1970), 61-74.
• [Ep] D. B. A. Epstein, Transversally hyperbolic 1-dimensional foliations, Astérisque 116 (1984), 53-69.
• [E] R. H. Escobales, Riemannian submersions with totally geodesic fibres, J. Differential Geom. 10 (1975), 253-276.
• [GP] K. Grove and P. Petersen V, Bounding homotopy types by geometry, Ann. of Math. 128 (1988), 195-208.
• [GPW] K. Grove, P. Petersen V and J.-Y. Wu, Geometric finiteness theorems via controlled topology, Invent. Math. 99 (1990), 205-213.
• [HK] E. Heintze and H. Karcher, A general comparison theorem with applications to volume estimates for submanifolds, Ann. Sci. Ecole Norm. Sup. 11 (1978), 451-470.
• [M] P. Molino, Riemannian Foliations, Birkhäuser, Boston 1988.
• [N] B. O'Neill, The fundamental equation of a submersion, Michigan Math. J. 13 (1966), 459-469.
• [P] S. Peters, Cheeger's finiteness theorem for diffeomorphism classes of Riemannian manifolds, J. Reine Angew. Math. 349 (1984), 77-82.
• [Rl] B. Reinhart, Foliated manifolds with bundle-like metrics, Ann. of Math. 69 (1959), 119-132.
• [R2] B. Reinhart, The Differential Geometry of Foliations, Springer, Berlin 1983.