On natural vector bundle morphisms over
A. Ntyam, A. Mba (2009)
Annales Polonici Mathematici
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Some properties and applications of natural vector bundle morphisms over are presented.
A. Ntyam, A. Mba (2009)
Annales Polonici Mathematici
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Some properties and applications of natural vector bundle morphisms over are presented.
Silvano Delladio (2011)
Annales Polonici Mathematici
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Let m,n be positive integers such that m < n and let G(n,m) be the Grassmann manifold of all m-dimensional subspaces of ℝⁿ. For V ∈ G(n,m) let denote the orthogonal projection from ℝⁿ onto V. The following characterization of purely unrectifiable sets holds. Let A be an -measurable subset of ℝⁿ with . Then A is purely m-unrectifiable if and only if there exists a null subset Z of the universal bundle such that, for all P ∈ A, one has . One can replace “for all P ∈ A” by “for...
J. Kurek, W. M. Mikulski (2010)
Annales Polonici Mathematici
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Let m and r be natural numbers and let be the rth order frame bundle functor. Let and be natural bundles, where . We describe all -natural operators A transforming sections σ of and classical linear connections ∇ on M into sections A(σ,∇) of . We apply this general classification result to many important natural bundles F and G and obtain many particular classifications.
J. Kurek, W. M. Mikulski (2007)
Annales Polonici Mathematici
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We classify all -natural operators transforming second order connections Γ: Y → J²Y on a fibred manifold Y → M into second order connections on the vertical Weil bundle corresponding to a Weil algebra A.
Frédéric Campana, Thomas Peternell (2011)
Bulletin de la Société Mathématique de France
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We first prove a strengthening of Miyaoka’s generic semi-positivity theorem: the quotients of the tensor powers of the cotangent bundle of a non-uniruled complex projective manifold have a pseudo-effective (instead of generically nef) determinant. A first consequence is that is of general type if its cotangent bundle contains a subsheaf with ‘big’ determinant. Among other applications, we deduce that if the universal cover of is not covered by compact positive-dimensional analytic...
Jan Kurek, Włodzimierz M. Mikulski (2012)
Annales Polonici Mathematici
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We prove that the problem of finding all -natural operators lifting classical linear connections ∇ on m-manifolds M to classical linear connections on the Weil bundle corresponding to a p-dimensional (over ℝ) Weil algebra A is equivalent to the one of finding all -natural operators transforming classical linear connections ∇ on m-manifolds M into base-preserving fibred maps .
Vikram B. Mehta, Christian Pauly (2007)
Bulletin de la Société Mathématique de France
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Let be a smooth projective curve of genus defined over an algebraically closed field of characteristic . Given a semistable vector bundle over , we show that its direct image under the Frobenius map of is again semistable. We deduce a numerical characterization of the stable rank- vector bundles , where is a line bundle over .
Włodzimierz M. Mikulski (2002)
Colloquium Mathematicae
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Let be the r-jet prolongation of the cotangent bundle of an n-dimensional manifold M and let be the dual vector bundle. For natural numbers r and n, a complete classification of all linear natural operators lifting 1-forms from M to 1-forms on is given.
Włodzimierz M. Mikulski (2003)
Annales Polonici Mathematici
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All natural operators A transforming a linear vector field X on a vector bundle E into a vector field A(X) on the r-jet prolongation of E are given. Similar results are deduced for the r-jet prolongations and in place of .
Anna Bednarska (2013)
Annales Universitatis Mariae Curie-Sklodowska, sectio A – Mathematica
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We describe all -natural operators transforming projectable-projectable classical torsion-free linear connections on fibred-fibred manifolds into classical linear connections on cotangent bundles of . We show that this problem can be reduced to finding -natural operators for , and , .
V. K. Kharchenko (2011)
Journal of the European Mathematical Society
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We give a complete classification of right coideal subalgebras that contain all grouplike elements for the quantum group provided that is not a root of 1. If has a finite multiplicative order ; this classification remains valid for homogeneous right coideal subalgebras of the Frobenius–Lusztig kernel . In particular, the total number of right coideal subalgebras that contain the coradical equals ; the order of the Weyl group defined by the root system of type .
Anna Bednarska (2011)
Annales Universitatis Mariae Curie-Sklodowska, sectio A – Mathematica
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We classify all -natural operators transforming projectable-projectable torsion-free classical linear connections on fibered-fibered manifolds of dimension into th order Lagrangians on the fibered-fibered linear frame bundle on . Moreover, we classify all -natural operators transforming projectable-projectable torsion-free classical linear connections r on fiberedfibered manifolds of dimension into Euler morphism on . These classifications can be expanded on...
Jiří M. Tomáš (2017)
Czechoslovak Mathematical Journal
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Let be an -dimensional manifold and a Weil algebra of height . We prove that any -covelocity , is determined by its values over arbitrary regular and under the first jet projection linearly independent elements of . Further, we prove the rigidity of the so-called universally reparametrizable Weil algebras. Applying essentially those partial results we give the proof of the general rigidity result without coordinate computations, which improves and generalizes the partial...
Jan Kurek, Włodzimierz Mikulski (2014)
Annales Universitatis Mariae Curie-Sklodowska, sectio A – Mathematica
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If is a Riemannian manifold, we have the well-known base preserving vector bundle isomorphism given by between the tangent and the cotangent bundles of . In the present note, we generalize this isomorphism to the one between the -th order vector tangent and the -th order cotangent bundles of . Next, we describe all base preserving vector bundle maps depending on a Riemannian metric in terms of natural (in ) tensor fields on .
Karl Oeljeklaus, Dan Zaffran (2006)
Bulletin de la Société Mathématique de France
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Let denote a holomorphic bundle with fiber and with basis . Both and are assumed to be Stein. For a Reinhardt bounded domain of dimension or , we give a necessary and sufficient condition on for the existence of a non-Stein such (Theorem ); for , we give necessary and sufficient criteria for to be Stein (Theorem ). For a Reinhardt bounded domain of any dimension not intersecting any coordinate hyperplane, we give a sufficient criterion for to be Stein (Theorem...
Manuela Chaves, Jesús García-Azorero (2006)
Journal of the European Mathematical Society
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We present some results concerning the problem , in , , where , , and is a smooth bounded domain containing the origin. In particular, bifurcation and uniqueness results are discussed.
Viorel Vâjâitu (2016)
Czechoslovak Mathematical Journal
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We consider a convexity notion for complex spaces with respect to a holomorphic line bundle over . This definition has been introduced by Grauert and, when is analytically trivial, we recover the standard holomorphic convexity. In this circle of ideas, we prove the counterpart of the classical Remmert’s reduction result for holomorphically convex spaces. In the same vein, we show that if separates each point of , then can be realized as a Riemann domain over the complex projective...
Takashi Noiri (1983)
Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti
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Si studiano le condizioni sotto cui l’immagine (o l'immagine inversa) di uno spazio localmente -chiuso sia localmente -chiuso.
Anna Bednarska (2012)
Annales Universitatis Mariae Curie-Sklodowska, sectio A – Mathematica
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We prove that any first order -natural operator transforming projectable general connections on an -dimensional fibred-fibred manifold into general connections on the vertical prolongation of is the restriction of the (rather well-known) vertical prolongation operator lifting general connections on a fibred manifold into (the vertical prolongation of ) on .
Jan Kurek, Włodzimierz M. Mikulski (2017)
Annales Universitatis Mariae Curie-Sklodowska, sectio A – Mathematica
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Let be the category of -dimensional manifolds and local diffeomorphisms and let be the tangent functor on . Let be the category of real vector spaces and linear maps and let be the category of -dimensional real vector spaces and linear isomorphisms. We characterize all regular covariant functors admitting -natural operators transforming classical linear connections on -dimensional manifolds into almost complex structures on .
W. M. Mikulski (2009)
Annales Polonici Mathematici
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We describe all -gauge-natural operators lifting right-invariant vector fields X on principal G-bundles P → M with m-dimensional bases into vector fields (X) on the rth order principal prolongation of P → M. In other words, we classify all -natural transformations covering the identity of , where is the r-jet prolongation of the Lie algebroid LP=TP/G of P, i.e. we find all -natural transformations which are similar to the Kumpera-Spencer isomorphism . We formulate axioms which...
Biagio Ricceri (2003)
Colloquium Mathematicae
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We deal with the problem ⎧ -Δu = f(x,u) + λg(x,u), in Ω, ⎨ () ⎩ where Ω ⊂ ℝⁿ is a bounded domain, λ ∈ ℝ, and f,g: Ω×ℝ → ℝ are two Carathéodory functions with f(x,0) = g(x,0) = 0. Under suitable assumptions, we prove that there exists λ* > 0 such that, for each λ ∈ (0,λ*), problem () admits a non-zero, non-negative strong solution such that for all p ≥ 2. Moreover, the function is negative and decreasing in ]0,λ*[, where is the energy functional related to (). ...
Qiaoling Xin, Lining Jiang, Zhenhua Ma (2015)
Czechoslovak Mathematical Journal
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Let be a finite group and a subgroup. Denote by (or ) the crossed product of and (or ) with respect to the adjoint action of the latter on the former. Consider the algebra generated by and , where we regard as an idempotent operator on for a certain conditional expectation of onto . Let us call the basic construction from the conditional expectation . The paper constructs a crossed product algebra , and proves that there is an algebra isomorphism between...
Hartmut von Trotha
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CONTENTSIntroduction................................................................................................................................... 5 Notations.......................................................................................................................... 5§ 1. Preliminaries........................................................................................................................ 6 1. Right invertible operators.....................................................................................................
A. R. Olfati (2016)
Commentationes Mathematicae Universitatis Carolinae
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Let be a zero-dimensional space and be the set of all continuous real valued functions on with countable image. In this article we denote by (resp., the set of all functions in with compact (resp., pseudocompact) support. First, we observe that (resp., ), where is the Banaschewski compactification of and is the -compactification of . This implies that for an -compact space , the intersection of all free maximal ideals in is equal to , i.e., . By applying...
Tamás Erdélyi (2003)
Studia Mathematica
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Denote by spanf₁,f₂,... the collection of all finite linear combinations of the functions f₁,f₂,... over ℝ. The principal result of the paper is the following. Theorem (Full Clarkson-Erdős-Schwartz Theorem). Suppose is a sequence of distinct positive numbers. Then is dense in C[0,1] if and only if . Moreover, if , then every function from the C[0,1] closure of can be represented as an analytic function on z ∈ ℂ ∖ (-∞, 0]: |z| < 1 restricted to (0,1). This result improves an...
Sevin Recillas (1984)
Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
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Si costruiscono curve di genere , che hanno fasci semicanonici tali che . Per si dimostra che gli sono molto ampi.
Romain Dujardin (2013)
Annales de la faculté des sciences de Toulouse Mathématiques
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Let be a holomorphic family of rational mappings of degree on , with marked critical points . To this data is associated a closed positive current of bidegree on , aiming to describe the simultaneous bifurcations of the marked critical points. In this note we show that the support of this current is accumulated by parameters at which eventually fall on repelling cycles. Together with results of Buff, Epstein and Gauthier, this leads to a complete characterization of . ...
Makoto Abe (2007)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
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Let be an open set of a Stein manifold of dimension such that for . We prove that is Stein if and only if every topologically trivial holomorphic line bundle on is associated to some Cartier divisor on .
Shaban Khidr, Osama Abdelkader (2017)
Czechoslovak Mathematical Journal
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Let be a -convex intersection, , , in a complex manifold of complex dimension , , and let be a holomorphic vector bundle of rank over . In this paper, -estimates, , for solutions to the -equation with small loss of smoothness are obtained for -valued -forms on when . In addition, we solve the -equation with a support condition in -spaces. More precisely, we prove that for a -closed form in , , , with compact support and for with there...