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Differential Geometry and its Applications, 2021 26 ...
Tomasz Goli'nski, F. Pelletier
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Morse theory on Banach manifolds [PDF]
Bulletin of the American Mathematical Society, 1970 AbstractLet ƒ be a C2 function on a C2 Banach manifold. A critical point x of ƒ is said to be weakly nondegenerate if there exists a neighborhood U of x and a hyperbolic linear isomorphism Lx: Tx(M) → Tx(M) such that in the coordinate system of U, dƒx + v(Lxv) > 0 if v ≠ 0.
Karen Uhlenbeck
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On hypersurfaces in a locally affine Riemannian Banach manifold [PDF]
International Journal of Mathematics and Mathematical Sciences, 2002 We prove that an essential hypersurface of second order in an infinite dimensional locally affine Riemannian Banach manifold is a Riemannian manifold of constant nonzero curvature.
El-Said R. Lashin, Tarek F. Mersal
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On the Banach Manifold of Simple Domains in the Euclidean Space and Applications to Free Boundary Problems [PDF]
Acta Applicandae Mathematicae - An International Survey Journal on Applying Mathematics and Mathematical Applications, 2019 In this paper we study the Banach manifold made up of simple C m + μ $C^{m+\mu }$ -domains in the Euclidean space R n $\mathbb{R}^{n}$ . This manifold is merely a topological or a C 0 $C^{0}$ Banach manifold not possessing a differentiable structure.
S. Cui
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Finite-dimensional complex manifolds on commutative Banach algebras and continuous families of compact complex manifolds [PDF]
Complex Manifolds, 2019 Let Γ(M) be the set of all global continuous cross sections of a continuous family M of compact complex manifolds on a compact Hausdorff space X. In this paper, we introduce a C(X)-manifold structure on Γ(M).
Yagisita Hiroki
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The Banach manifold C(M,N) [PDF]
Differential Geometry and its Applications, 2018 Let $M$ be a closed manifold and let $N$ be a connected manifold without boundary. For each $k\in\mathbb{N}$ the set of $k$ times continuously differentiable maps between $M$ and $N$ has the structure of a smooth Banach manifold where the underlying manifold topology is the compact-open $C^k$ topology.
J. Wittmann
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On analytic manifolds belonging to a Banach algebra
Indagationes Mathematicae (Proceedings), 1969 AbstractA certain kind of analytic manifold belonging to a Banach algebra is introduced. These manifolds can always be embedded in principal extensions of Riemann surfaces.
S.T.M. Ackermans
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Hereditary Ball-Covers for Some Banach Manifolds [PDF]
Proceedings of the American Mathematical Society, 1972 At a problem seminar in Ithaca, New York, during January 1969, James Eells raised the question (numbered 33 on the circulated list) of whether a paracompact Fréchet manifold admits a locally finite cover by open sets, all of whose intersections are contractible.
James E. West
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The Banach manifold structure of the space of metrics on noncompact manifolds
Differential Geometry and its Applications, 1991 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
J. Eichhorn
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Characterization of a Banach-Finsler manifold in terms of the algebras of smooth functions [PDF]
, 2011 In this note we give sufficient conditions to ensure that the weak Finsler structure of a complete C-k Finsler manifold M is determined by the normed algebra C-b(k)(M) of all real-valued, bounded and C-k smooth functions with bounded derivative defined ...
J. Jaramillo +2 more
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