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On the conformal relation between twistors and Killing spinors

Friedrich, Thomas (1990)

Proceedings of the Winter School "Geometry and Physics"

[For the entire collection see Zbl 0699.00032.] The author considers the conformal relation between twistors and spinors on a Riemannian spin manifold of dimension n ≥ 3 . A first integral is constructed for a twistor spinor and various geometric properties of the spin manifold are deduced. The notions of a conformal deformation and a Killing spinor are considered and such a deformation of a twistor spinor into a Killing spinor and conditions for the equivalence of these quantities is indicated.

On the Conley index in Hilbert spaces in the absence of uniqueness

Marek Izydorek, Krzysztof P. Rybakowski (2002)

Fundamenta Mathematicae

Consider the ordinary differential equation (1) ẋ = Lx + K(x) on an infinite-dimensional Hilbert space E, where L is a bounded linear operator on E which is assumed to be strongly indefinite and K: E → E is a completely continuous but not necessarily locally Lipschitzian map. Given any isolating neighborhood N relative to equation (1) we define a Conley-type index of N. This index is based on Galerkin approximation of equation (1) by finite-dimensional ODEs and extends...

On the Curvature and Heat Flow on Hamiltonian Systems

Shin-ichi Ohta (2014)

Analysis and Geometry in Metric Spaces

We develop the differential geometric and geometric analytic studies of Hamiltonian systems. Key ingredients are the curvature operator, the weighted Laplacian, and the associated Riccati equation.We prove appropriate generalizations of the Bochner-Weitzenböck formula and Laplacian comparison theorem, and study the heat flow.

On the Darboux transformation. II.

Veronika Chrastinová (1995)

Archivum Mathematicum

Automorphisms of the family of all Sturm-Liouville equations y ' ' = q y are investigated. The classical Darboux transformation arises as a particular case of a general result.

On the differential form spectrum of hyperbolic manifolds

Gilles Carron, Emmanuel Pedon (2004)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

We give a lower bound for the bottom of the L 2 differential form spectrum on hyperbolic manifolds, generalizing thus a well-known result due to Sullivan and Corlette in the function case. Our method is based on the study of the resolvent associated with the Hodge-de Rham laplacian and leads to applications for the (co)homology and topology of certain classes of hyperbolic manifolds.

On the differential geometry of some classes of infinite dimensional manifolds

Maysam Maysami Sadr, Danial Bouzarjomehri Amnieh (2024)

Archivum Mathematicum

Albeverio, Kondratiev, and Röckner have introduced a type of differential geometry, which we call lifted geometry, for the configuration space Γ X of any manifold X . The name comes from the fact that various elements of the geometry of Γ X are constructed via lifting of the corresponding elements of the geometry of X . In this note, we construct a general algebraic framework for lifted geometry which can be applied to various “infinite dimensional spaces” associated to X . In order to define a lifted...

On the distribution of resonances for some asymptotically hyperbolic manifolds

R. G. Froese, Peter D. Hislop (2000)

Journées équations aux dérivées partielles

We establish a sharp upper bound for the resonance counting function for a class of asymptotically hyperbolic manifolds in arbitrary dimension, including convex, cocompact hyperbolic manifolds in two dimensions. The proof is based on the construction of a suitable paramatrix for the absolute S -matrix that is unitary for real values of the energy. This paramatrix is the S -matrix for a model laplacian corresponding to a separable metric near infinity. The proof of the upper bound on the resonance...

Currently displaying 321 – 340 of 622