The Bonnet-Meyers theorem is true for Riemann Hilbert Manifolds.
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Lars Andersson (1986)
Mathematica Scandinavica
Tudor Ratiu, Yakov Eliashberg (1991)
Inventiones mathematicae
Antony Tromba (1976)
Mémoires de la Société Mathématique de France
Ivan Kolář, Marco Modungo (1998)
Annales Polonici Mathematici
Two fiber bundles E₁ and E₂ over the same base space M yield the fibered set ℱ(E₁,E₂) → M, whose fibers are defined as , for each x ∈ M. This fibered set can be regarded as a smooth space in the sense of Frölicher and we construct its tangent prolongation. Then we extend the Frölicher-Nijenhuis bracket to projectable tangent valued forms on ℱ(E₁,E₂). These forms turn out to be a kind of differential operators. In particular, we consider a general connection on ℱ(E₁,E₂) and study the associated...
Tomoyoshi Yoshida (1985)
Inventiones mathematicae
Kaveh Eftekharinasab (2015)
Communications in Mathematics
In this paper we study Lipschitz-Fredholm vector fields on bounded Fréchet-Finsler manifolds. In this context we generalize the Morse-Sard-Brown theorem, asserting that if is a connected smooth bounded Fréchet-Finsler manifold endowed with a connection and if is a smooth Lipschitz-Fredholm vector field on with respect to which satisfies condition (WCV), then, for any smooth functional on which is associated to , the set of the critical values of is of first category in . Therefore,...
Esteban Andruchow, Gabriel Larotonda (2010)
Studia Mathematica
Let = u: u unitary and u-1 compact stand for the unitary Fredholm group. We prove the following convexity result. Denote by the rectifiable distance induced by the Finsler metric given by the operator norm in . If and the geodesic β joining u₀ and u₁ in satisfy , then the map is convex for s ∈ [0,1]. In particular, the convexity radius of the geodesic balls in is π/4. The same convexity property holds in the p-Schatten unitary groups = u: u unitary and u-1 in the p-Schatten class...
Esrafilian, Ebrahim, Salimi Moghaddam, Hamid Reza (2006)
SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]
E. Binz (1980)
Monatshefte für Mathematik
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