Results 1 to 10 of about 92,207 (169)

On complex Banach manifolds similar to Stein manifolds [PDF]

arXiv, 2010
We give an abstract definition, similar to the axioms of a Stein manifold, of a class of complex Banach manifolds in such a way that a manifold belongs to the class if and only if it is biholomorphic to a closed split complex Banach submanifold of a separable Banach space.
Patyi, Imre
arxiv   +9 more sources

Regulated curves on a Banach manifold and singularities of endpoint map. I. Banach manifold structure [PDF]

Differential Geometry and its Applications, Volume 99, 2025, 102245, 2021
We consider regulated curves in a Banach bundle whose projection on the basis is continuous with regulated derivative. We build a Banach manifold structure on the set of such curves. This result was previously obtained for the case of strong Riemannian Banach manifold and absolutely continuous curves in arXiv:1612.02604. The essential argument used was
Tomasz Goliński, Fernand Pelletier
arxiv   +5 more sources

On Sussmann theorem for orbits of sets of vector fields on Banach manifolds [PDF]

arXiv, 2011
The purpose of this paper is to give some generalizations, in the context of Banach mani- folds, of Sussmann's results about the orbits of families of vector fields ([Su]). Essentially, we define the notion of "l1-orbits" for any family of vector fields on a Banach manifold, and we prove, under appropriate assumptions, that such an orbit is a weak ...
Lathuille, Arnauld, Pelletier, Fernand
arxiv   +5 more sources

On real analytic Banach manifolds [PDF]

Journal of the London Mathematical Society, 2008
Let $X$ be a real Banach space with an unconditional basis (e.g., $X=\ell_2$ Hilbert space), $\Omega\subset X$ open, $M\subset\Omega$ a closed split real analytic Banach submanifold of $\Omega$, $E\to M$ a real analytic Banach vector bundle, and ${\Cal A}
Patyi, Imre, Simon, Scott
core   +5 more sources

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
openalex   +5 more sources

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
doaj   +2 more sources

Observational Banach Manifolds [PDF]

Journal of Applied Environmental and Biological Sciences, 4(12)237-247, 2014, 2014
In this paper, the concept of selective real manifolds is extended. It is proved that the product of two selective Banach manifolds is a selective Banach manifold. The notion of the $\alpha$--level differentiation of the mappings between selective Banach manifolds is presented. Basic properties of $(r, \alpha)$--differentiable maps are studied. Tangent
Mehrpoya, Mohammad, Molaei, Mohammadreza
arxiv   +3 more sources

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
doaj   +2 more sources

Chaos and shadowing around a homoclinic tube [PDF]

Abstract and Applied Analysis, 2003
Let F be a C3 diffeomorphism on a Banach space B. F has a homoclinic tube asymptotic to an invariant manifold. Around the homoclinic tube, Bernoulli shift dynamics of submanifolds is established through a shadowing lemma. This work removes an uncheckable
Yanguang (Charles) Li
doaj   +6 more sources

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
openalex   +4 more sources